Method of using G-matrix Fourier transformation nuclear magnetic resonance (GFT NMR) spectroscopy for rapid chemical shift assignment and secondary structure determination of proteins

ABSTRACT

The present invention presents a new approach to rapidly obtaining precise high-dimensional NMR spectral information, named “GFT NMR spectroscopy”, which is based on the phase sensitive joint sampling of the indirect dimensions spanning a subspace of a conventional NMR experiment. The phase-sensitive joint sampling of several indirect dimensions of a high-dimensional NMR experiment leads to largely reduced minimum measurement times when compared to FT NMR. This allows one to avoid the “sampling limited” data collection regime. Concomitantly, the analysis of the resulting chemical shift multiplets, which are edited by the G-matrix transformation, yields increased precision for the measurement of the chemical shifts. Additionally, methods of conducting specific GFT NMR experiments as well as methods of conducting a combination of GFT NMR experiments for rapidly obtaining precise chemical shift assignment and determining the structure of proteins or other molecules are disclosed.

[0001] The present invention claims the benefit of U.S. ProvisionalPatent Application Serial Nos. 60/395,591, filed Jul. 11, 2002, and60/441,385, filed Jan. 16, 2003, which are hereby incorporated byreference in their entirety. This invention arose out of researchsponsored by the National Science Foundation (Grant No. MCB 0075773) andNational Institutes of Health (Grant No. P50 GM62413-01). The U.S.Government may have certain rights in this invention.

FIELD OF THE INVENTION

[0002] The present invention relates to methods of using G-matrixFourier transformation nuclear magnetic resonance (GFT NMR) spectroscopyfor rapidly obtaining and connecting precise chemical shift values anddetermining the structure of proteins and other molecules.

BACKGROUND OF THE INVENTION

[0003] Nuclear magnetic resonance (NMR) (Ernst et al., Principles ofNuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford(1987); Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, N.Y. (1986);Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego(1996))-based structural studies rely on two broad classes ofexperimental radio-frequency pulse schemes for recording two-dimensional(2D) (Ernst et al., Principles of Nuclear Magnetic Resonance in One andTwo Dimensions, Clarendon, Oxford (1987)), three-dimensional (3D)(Oschkinat et al., Nature, 332:374-376 (1988)), or four-dimensional (4D)(Kay et al., Science, 249:411-414 (1990)) Fourier transformation (FT)NMR spectra. Correlation spectroscopy (COSY) delineates exclusivelyscalar coupling connectivities to measure chemical shifts, and(heteronuclear resolved) ¹H, ¹H-nuclear Overhauser enhancementspectroscopy (NOESY) reveals the strength of through-space dipolarcouplings of ¹H spins to estimate distances (Ernst et al., Principles ofNuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford(1987); Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, N.Y.(1986)). NMR spectra need to exhibit (i) signal-to-noise (S/N) ratioswarranting reliable data interpretation, (ii) digital resolutionsensuring adequate precision for the measurement of NMR parameters suchas chemical shifts, and (iii) a dimensionality at which a sufficientnumber of NMR parameters is correlated (Ernst et al., Principles ofNuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford(1987); Cavanagh et al., Protein NMR Spectroscopy, Academic Press, SanDiego (1996)). While increased intensity of NOESY peaks ensures theirmore accurate integration (which, in turn, may translate into increasedaccuracy of the NMR structure), the mere identification of COSY peakssuffices to obtain the desired chemical shifts. Hence, COSY peaksignal-to noise ratios larger that ˜3:1 reflect, in essence,inappropriately long measurement times. Moreover, the total number ofpeaks in COSY grows only linearly with the number of spins involved andis, for a defined magnetization transfer pathway, “independent” of thedimensionality N. Thus, a minimal “target dimensionality” N_(t) at whichmost of the COSY peaks detected for a given molecule are resolved can bedefined. Further increased dimensionality does not aim at resolving peakoverlap but at increasing the number of correlations obtained in asingle data set. This eliminates ambiguities when severalmultidimensional NMR spectra are combined for resonance assignment, forexample, when using ¹H, ¹³C, ¹⁵N triple-resonance NMR to assign proteinresonances (Cavanagh et al., Protein NMR Spectroscopy, Academic Press,San Diego (1996)).

[0004] An increase in dimensionality is, however, limited by the need toindependently sample the indirect dimensions, because this leads tolonger measurement times. Although the measurement time can be somewhatreduced by aliasing signals (Cavanagh et al., Protein NMR Spectroscopy,Academic Press, San Diego (1996)) or accepting a lower digitalresolution in the indirect dimensions, high dimensionality oftenprevents one from tuning the measurement time to a value that ensures toobtain sufficient, but not unnecessarily large S/N ratios.

[0005] In view of these considerations, “sampling” and “sensitivitylimited” data collection regimes are defined (Szyperski et al., Proc.Natl. Acad. Sci. USA, 99:8009-8014 (2002)), depending on whether thesampling of the indirect dimensions or the sensitivity of the FT NMRexperiment determines the minimal measurement time. In the sensitivitylimited regime, long measurement times are required to achievesufficient S/N ratios, so that the sampling of indirect dimensions isnot necessarily constraining the adjustment of the measurement time. Inthe sampling limited regime, some or even most of the instrument time isinvested for sampling, which yields excessively large S/N ratios. Inview of the ever increasing sensitivity of NMR instrumentation, newmethodology to avoid the sampling limited regime is needed. (Szyperskiet al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002)).

[0006] In general, phase-sensitive acquisition of an N-dimensional (ND)FT NMR experiment (Ernst et al., Principles of Nuclear MagneticResonance in One and Two Dimensions, Clarendon, Oxford (1987); Cavanaghet al., Protein NMR Spectroscopy, Academic Press, San Diego (1996))requires sampling of N−1 indirect dimensions with n₁×n2 . . . n_(N−1)complex points representing$n_{FID} = {2^{N - 1} \cdot {\prod\limits_{j = 1}^{N - 1}\quad n_{j}}}$

[0007] free induction decays (FIDs). The resulting steep increase of theminimal measurement time, T_(m), with dimensionality prevents one fromrecording five- or higher-dimensional FT NMR spectra: acquiring 16complex points in each indirect dimension (with one scan per FID eachsecond) yields T_(m)(3D)=0.5 hour, T_(m)(4D)=9.1 hours, T_(m)(5D)=12days, and T_(m)(6D)=1.1 years.

[0008] Thus, higher-dimensional FT NMR spectroscopy suffers from twomajor drawbacks: (i) The minimal measurement time of an ND FT NMRexperiment, which is constrained by the need to sample N−1 indirectdimensions, may exceed by far the measurement time required to achievesufficient signal-to-noise ratios. (ii) The low resolution in theindirect dimensions severely limits the precision of the indirectchemical shift measurements.

[0009] The present invention is directed to overcoming the deficienciesin the art.

SUMMARY OF THE INVENTION

[0010] The present invention relates to a method of conducting a (N,N−K)dimensional (D) G-matrix Fourier transformation (GFT) nuclear magneticresonance (NMR) experiment, where N is the dimensionality of anN-dimensional (ND) Fourier transformation (FT) NMR experiment and K isthe desired reduction in dimensionality relative to N. The methodinvolves providing a sample and applying radiofrequency pulses for theND FT NMR experiment to the sample. Then, m indirect chemical shiftevolution periods of the ND FT NMR experiment are selected, where mequals K+1, and the m indirect chemical shift evolution periods arejointly sampled. Next, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate (N−K)D basic NMRspectra containing frequency domain signals with 2^(K) chemical shiftmultiplet components, thereby enabling phase-sensitive sampling of alljointly sampled m indirect chemical shift evolution periods. Finally,the (N−K) D basic NMR spectra are transformed into (N−K) Dphase-sensitively edited basic NMR spectra, where the 2^(K) chemicalshift multiplet components of the (N−K) D basic NMR spectra are editedto yield (N−K) D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

[0011] Another aspect of the present invention relates to a method forsequentially assigning chemical shift values of an α-proton, ¹H^(α), anα-carbon, ¹³C^(α), a polypeptide backbone carbonyl carbon, ¹³C′, apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H^(N), of a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (5,2)D [HACACONHN] GFT NMR experiment tomeasure and connect the chemical shift values of the α-proton of aminoacid residue i−1, ¹H^(α) _(i−1), the at-carbon of amino acid residuei−1, ¹³C^(α) _(i−1), the polypeptide backbone carbonyl carbon of aminoacid residue i−1, ¹³C′_(i−1), the polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i), and the polypeptide backbone amide protonof amino acid residue i, ¹H^(N) _(i) and (2) a (5,2)D [HACA,CONHN] GFTNMR experiment to measure and connect the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), the polypeptide backboneamide nitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, ¹H^(N) _(i−1). Then,sequential assignments of the chemical shift values of ¹H^(α,) ¹³C^(α,)¹³C′, ¹⁵N, and ¹H^(N) are obtained by (i) matching the chemical shiftvalues of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the(5,2)D [HACACONHN] GFT NMR experiment with the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the (5,2)D[HACACONHN] GFT NMR experiment, (ii) using the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) to identify the type ofamino acid residue i−1, and (iii) mapping sets of sequentially connectedchemical shift values to the amino acid sequence of the polypeptidechain and using the chemical shift values to locate secondary structureelements within the polypeptide chain.

[0012] Yet another aspect of the present invention relates to a methodfor sequentially assigning chemical shift values of an α-proton, ¹H^(α),an α-carbon, ¹³C^(α), a polypeptide backbone carbonyl carbon, ¹³C′, apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H^(N), of a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (5,3)D [HACACONHN] GFT NMR experiment tomeasure and connect the chemical shift values of the α-proton of aminoacid residue i−1, ¹H^(α) _(i−1), the α-carbon of amino acid residue i−1,¹³C^(α) _(i−1), the polypeptide backbone carbonyl carbon of amino acidresidue i−1, ¹³C′_(i−1), the polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i), and the polypeptide backbone amide protonof amino acid residue i, ¹H^(N) _(i) and (2) a (5,3)D [HACA,CONHN] GFTNMR experiment to measure and connect the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), the polypeptide backboneamide nitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, ¹H^(N) _(i−1). Then,sequential assignments of the chemical shift values of ¹H^(α), ¹³C^(α),¹³C′, ¹⁵N, and ¹H^(N) are obtained by (i) matching the chemical shiftvalues of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the(5,3)D [HACACONHN] GFT NMR experiment with the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the (5,3)D[HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) to identify the type ofamino acid residue i−1, and (iii) mapping sets of sequentially connectedchemical shift values to the amino acid sequence of the polypeptidechain and using the chemical shift values to locate secondary structureelements within the polypeptide chain.

[0013] A further aspect of the present invention relates to a method forsequentially assigning chemical shift values of α- and β-carbons,¹³C^(α/β), a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptidebackbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton,¹H^(N), of a protein molecule. The method involves providing a proteinsample and conducting a set of G matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (4,3)D [CBCACONHN] GFT NMR experiment to measure andconnect the chemical shift values of the α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i−1), the polypeptide backbone carbonyl carbonof amino acid residue i−1, ¹³C′_(i−1), the polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i), and the polypeptide backboneamide proton of amino acid residue i, ¹H^(N) _(i) and (2) a (4,3)D[CBCA,CONHN] GFT NMR experiment to measure and connect the chemicalshift values of ¹³C^(α/β) _(i−1), ¹³C′_(i−1), the polypeptide backboneamide nitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, ¹H^(N) _(i−1). Then,sequential assignments of the chemical shift values of ¹³C^(α/β), ¹³C′,¹⁵N, and ¹H^(N) are obtained by (i) matching the chemical shift valuesof ¹³C^(α/β) _(i−1) and ¹³C′_(i−1) measured by the (4,3)D [CBCACONHN]GFT NMR experiment with the chemical shift values of ¹³C^(α/β) _(i−1)and ¹³C′_(i−1) measured by the (4,3)D [CBCA,CONHN] GFT NMR experiment,(ii) using the chemical shift values of ¹³C^(α/β) _(i−1), and ¹³C′_(i−1)to identify the type of amino acid residue i−1, and (iii) mapping setsof sequentially connected chemical shift values to the amino acidsequence of the polypeptide chain and using the chemical shift values tolocate secondary structure elements within the polypeptide chain.

[0014] The present invention also relates to a method for sequentiallyassigning chemical shift values of α- and β-carbons, ¹³C^(α/β), apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H^(N), of a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment tomeasure and connect the chemical shift values of the α- and β-carbons ofamino acid residue i−1, ¹³C^(α/β) _(i−1), the α-carbon of amino acidresidue i−1, ¹³C^(α) _(i−1), the polypeptide backbone amide nitrogen ofamino acid residue i−1, ¹⁵N_(i−1), and the polypeptide backbone amideproton of amino acid residue i−1, ¹H^(N) _(i−1) and (2) a GFT NMRexperiment selected from the group consisting of a (4,3)D[HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMRexperiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment tomeasure and connect the chemical shift values of ¹³C^(α/β) _(i−1),¹³C^(α) _(i−1), the polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i), and the polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i). Then, sequential assignments of thechemical shift values of ¹³C^(α/β), ¹⁵N, and ¹H^(N) are obtained by (i)matching the chemical shift values of ¹³C^(α/β) _(i−1) measured by theGFT NMR experiment selected from the group consisting of a (4,3)D[HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMRexperiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment with thechemical shift values of ¹³C^(α/β) _(i−1) measured by the (4,3)D[HNNCACBCA] GFT NMR experiment, (ii) using the chemical shift values of¹³C^(α/β) _(i−1) to identify the type of amino acid residue i−1, and(iii) mapping sets of sequentially connected chemical shift values tothe amino acid sequence of the polypeptide chain and using the chemicalshift values to locate secondary structure elements within thepolypeptide chain.

[0015] Another aspect of the present invention relates to a method forassigning chemical shift values of γ-, δ-, and ε-aliphatic sidechainprotons, ¹H^(γ/δ/ε), and chemical shift values of γ-, δ-, andε-aliphatic sidechain carbons located peripheral to β-carbons,¹³C^(γ/δ/ε), of a protein molecule. The method involves providing aprotein sample and conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (5,3)D [HCC,CH—COSY] GFT NMR experiment to measure andconnect the chemical shift values of a proton of amino acid residue i−1,¹H_(i−1), a carbon of amino acid residue i−1 coupled to ¹H_(i−1),¹³C_(i−1), a carbon coupled to ¹³C_(i−1), ¹³C_(i−1) ^(coupled), and aproton coupled to ¹³C_(i−1) ^(coupled), ¹H_(i−1) ^(coupled), and (2) a(5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect thechemical shift values of α- and β-protons of amino acid residue i−1,¹H^(α/β) _(i−1), and α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1). Then, assignments of the chemical shift values of¹H^(γ/δ/ε) and ¹³C^(γ/δ/ε) are obtained by (i) identifying ¹H_(i−1),¹³C_(i−1), ¹³C_(i−1) ^(coupled), and ¹H_(i−1) ^(coupled) measured by the(5,3)D [HCC,CH—COSY] GFT NMR experiment as ¹H^(α) _(i−1), ¹³C^(α)_(i−1), ¹³C^(β) _(i−1), and ¹H^(β) _(i−1), respectively, and therebymatching the chemical shift values of ¹H^(α/β) _(i−1), and ¹³C^(α/β)_(i−1) with the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and(ii) using the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) in conjunction with other chemical shift connections from the(5,3)D [HCC,CH—COSY] GFT NMR experiment to measure the chemical shiftvalues of ¹H^(γ/δ/ε) _(i−1) and ¹³C^(γ/δ/ε) _(i−1).

[0016] Yet another aspect of the present invention relates to a methodfor assigning chemical shift values of γ-, δ-, and ε-aliphatic sidechainprotons, ¹H^(γ/δ/ε), and chemical shift values of γ-, δ-, andε-aliphatic sidechain carbons located peripheral to β-carbons,¹³C^(γ/δε), of a protein molecule. The method involves providing aprotein sample and conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (4,2)D [HCCH—COSY] GFT NMR experiment to measure andconnect the chemical shift values of a proton of amino acid residue i−1,¹H_(i−1), a carbon of amino acid residue i−1 coupled to ¹H_(i−1),¹³C_(i−1), a carbon coupled to ¹³C_(i−1), ¹³C_(i−1) ^(coupled), and aproton coupled to ¹³C_(i−1) ^(coupled), ¹H_(i−1) ^(coupled), and (2) a(5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect thechemical shift values of α- and β-protons of amino acid residue i−1,¹H^(α/β) _(i−1), and α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1). Then, assignments of the chemical shift values of¹H^(γ/δ/ε) and ¹³C^(γ/δ/ε) are obtained by (i) identifying ¹H_(i−1),¹³C_(i−1), ¹³C_(i−1) ^(coupled), and ¹H^(N) _(i−1) ^(coupled) measuredby the (4,2)D [HCCH—COSY] GFT NMR experiment as ¹H^(α) _(i−1), C^(α)_(i−1), ¹³C^(β) _(i−1), and ¹H^(β) _(i−1) respectively, and therebymatching the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) with the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and(ii) using the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) in conjunction with other chemical shift connections from the(4,2)D [HCCH—COSY] GFT NMR experiment to measure the chemical shiftvalues of ¹H^(γ/δ/ε) _(i−1) and 3C^(γ/δ/ε) _(i−1).

[0017] A further aspect of the present invention relates to a method forassigning chemical shift values of a γ-carbon, ¹³C^(γ), a δ-carbon,¹³C^(δ), and a δ-proton, ¹H^(δ), of an amino acid residue containing anaromatic spin system in a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (5,3)D [HBCBCGCDHD] GFT NMR experimentto measure and connect the chemical shift values of a β-proton of aminoacid residue i−1, ¹H^(β) _(i−1), a β-carbon of amino acid residue i−1,¹³C^(β) _(i−1), a γ-carbon of amino acid residue i−1, ¹³C^(γ) _(i−1), aδ-carbon of amino acid residue i−1, ¹³C^(δ) _(i−1), and a δ-proton ofamino acid residue i−1, ¹H^(δ) _(i−1), and (2) a (5,3)D[HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect thechemical shift values of ¹H^(β) _(i−1) and ¹³C^(β) _(i−1). Then,assignments of the chemical shift values of ¹³C^(γ), ¹³C^(δ), and ¹H^(δ)are obtained by (i) matching the chemical shift values of ¹H^(β) _(i−1)and ¹³C^(β) _(i−1) measured by the (5,3)D HBCBCACA(CO)NHN GFT NMRexperiment with the chemical shift values of ¹H^(β) _(i−1) and ¹³C^(β)_(i−1), measured by the (5,3)D [HBCBCGCDHD] GFT NMR experiment, and (ii)using the chemical shift values of ¹³C^(γ), ¹³C^(δ), and ¹H^(δ) toidentify the type of amino acid residue containing the aromatic spinsystem.

[0018] The present invention also relates to a method for assigningchemical shift values of aliphatic and aromatic protons and aliphaticand aromatic carbons of an amino acid residue containing aliphatic andaromatic spin systems in a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a first GFT NMR experiment, which isselected from the group consisting of a (5,3)D [HCC,CH—COSY] GFT NMRexperiment, a (4,2)D [HCCH—COSY] GFT NMR experiment, a (5,2)D[HCCCH—COSY] GFT NMR experiment, and a (5,3)D [HCCCH—COSY] GFT NMRexperiment and is acquired for the aliphatic spin system, to measure andconnect the chemical shift values of α- and β-protons of amino acidresidue i, ¹H^(α/β) _(i), α- and β-carbons of amino acid residue i,¹³C^(α/β) _(i), a δ-carbon of amino acid residue i, ¹³C^(γ) _(i), and(2) a second GFT NMR experiment, which is selected from the groupconsisting of a (5,3)D [HCC,CH—COSY] GFT NMR experiment, a (4,2)D[HCCH—COSY] GFT NMR experiment, a (5,2)D [HCCCH—COSY] GFT NMRexperiment, and a (5,3)D [HCCCH—COSY] GFT NMR experiment and is acquiredfor the aromatic spin system, to measure and connect the chemical shiftvalues of ¹³C^(γ) _(i) and other aromatic protons and carbons of aminoacid residue i. Then, assignments of the chemical shift values of thealiphatic and aromatic protons and aliphatic and aromatic carbons areobtained by matching the chemical shift value of ¹³C^(γ) _(i) measuredby the first GFT NMR experiment with the chemical shift value of ¹³C^(γ)_(i) measured by the second GFT NMR experiment.

[0019] Another aspect of the present invention relates to a method forobtaining assignments of chemical shift values of ¹H, ¹³C, and ¹⁵N of aprotein molecule. The method involves providing a protein sample andconducting five G matrix Fourier transformation (GFT) nuclear magneticresonance (NMR) experiments on the protein sample, where (1) a firstexperiment is a (4,3)D [HNNCACBCA] GFT NMR experiment for obtainingintraresidue correlations of chemical shift values; (2) a secondexperiment is a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment forobtaining interresidue correlations of chemical shift values; (3) athird experiment is a (5,3)D [HCC,CH—COSY] GFT NMR experiment forobtaining assignments of aliphatic sidechain chemical shift values; (4)a fourth experiment is a (5,3)D [HBCBCGCDHD] GFT NMR experiment forlinking chemical shift values of aliphatic protons, ¹H^(β) and ¹³C^(β),and aromatic protons, ¹³C^(δ) and ¹H^(δ); and (5) a fifth experiment isa (4,2)D [HCCH—COSY] GFT NMR experiment for obtaining assignments ofaromatic sidechain chemical shift values.

[0020] The present invention discloses a number of specific GFT NMRexperiments and different combinations of those experiments which allowsone to obtain sequential backbone chemical shift assignments fordetermining the secondary structure of a protein molecule and completeassignments of chemical shift values for a protein molecule includingaliphatic and aromatic sidechain spin systems.

[0021] The present invention provides a generally applicable approachfor NMR data acquisition and processing named “GFT NMR spectroscopy”.This approach is based on the phase-sensitive joint sampling of severalindirect dimensions while ensuring that all chemical shift correlationsare retained. The employment of GFT NMR focuses on the sampling limiteddata collection regime and, considering that NMR measurements longerthan about a week are impracticable, on the acquisition of five- orhigher-dimensional spectral information.

[0022] GFT NMR relaxes on constraints arising from two major drawbacksof FT NMR, that is, the problem of having excessive or prohibitivelylong measurement times due to sampling of indirect dimensions and thelimited precision of chemical shift measurements in the indirectdimensions arising from comparably low digital resolution. Within a fewhours or less, GFT NMR spectroscopy affords the correlations of evenfive- or higher-dimensional FT NMR spectra acquired with high digitalresolution. Thus, GFT NMR spectroscopy allows one to tune measurementtimes to sensitivity requirements without compromising on thedimensionality or the digital resolution. High-throughput efforts suchas NMR-based structural genomics (Montelione et al., Nat. Struct. Biol.,7:982-984 (2000), which is hereby incorporated by reference in itsentirety) will profit from this feature, because automated resonanceassignment (Szyperski et al., J. Biomol. NMR, 11:387-405 (1998); Moseleyet al, Curr. Opin. Struct. Biol., 9:635-642 (1999); Moseley et al.,Methods Enzymol., 339:91-108 (2001), which are hereby incorporated byreference in their entirety) benefits from maximizing the number ofcorrelations obtained from in a single NMR experiment. Moreover, therapid sampling realized with GFT NMR spectroscopy will allow researchersto obtain highest dimensional NMR information with exceptional timeresolution when, for example, studying slow protein folding in real time(Dyson et al., Annu. Rev. Phys. Chem., 47:369-395 (1996), which ishereby incorporated by reference in its entirety). The high precision ofthe chemical shift measurements is of potential importance for a broadrange of NMR applications in natural sciences and engineering, forexample, for automated assignment, or when studying systems with highchemical shift degeneracy such as RNA ribose spin systems (Cromsigt etal., Methods Enzymol., 338:371-399 (2001), which is hereby incorporatedby reference in its entirety), (partially) unfolded proteins (Neri etal., FEBS Lett., 303:129-135 (1992), which is hereby incorporated byreference in it its entirety), or lipids (Wang et al., Biochemistry,41:5453-5461 (2002), which is hereby incorporated by reference in itsentirety). Finally, the high precision of the shift measurements may berecruited to accurately measure other NMR parameters such as residualdipolar couplings for structural refinement (Tjandra et al., Science,278:1111-1114 (1997); Prestegard, Nat. Struct. Biol., 5:517-522 (1998),which are hereby incorporated by reference in their entirety), andtransverse relaxation optimized (Pervushin et al., Proc. Natl. Acad.Sci. USA, 94:12366-12371 (1997), which is hereby incorporated byreference in its entirety) GFT NMR may develop into a powerful approachto investigate larger systems.

[0023] In the sensitivity limited regime, GFT NMR may be advantageous incases where an extended radiofrequency (rf) phase cycle is desirable forspectral editing and/or improved artifact suppression (Cavanagh et al.,Protein NMR Spectroscopy, Academic Press, San Diego (1996), which ishereby incorporated by reference in its entirety).

BRIEF DESCRIPTION OF THE DRAWINGS

[0024]FIG. 1 compares the conventional sampling of a 3D time domainsubspace of an ND FT NMR experiment (on the left) with thephase-sensitive joint sampling of the three dimensions in an (N,N-2)DGFT NMR (on the right), that is, with K=2. Processing of the FT NMRexperiment requires a 3D FT of the subspace, while the GFT NMRexperiment requires time domain editing of chemical shift multipletcomponents by application of the so-called G-matrix (see equation 1 inthe “Detailed Description of the Invention”) and ID FT of the resultingp=2^(K+1) data sets. For the GFT NMR experiment, the phase settings ofø₁ and ø₂ of the rf pulses creating transverse magnetization forfrequency labeling with Ω₁ and Ω₂ are indicated for basic spectra (topfour rows), first-order central peak spectra (two rows in the middle),and the second-order central peak spectrum (bottom row). Instead of asingle peak in FT NMR which encodes three chemical shifts, one obtains ap-fold overdetermined system of equations. A least-squares fitcalculation yields the three shifts from the position of seven peaks. Ina GFT NMR experiment with constant-time chemical shift evolutionperiods, the lines forming the chemical shift multiplets have the samewidth as the resonances in FT NMR (if recorded with correspondingmaximal evolution times; see also FIGS. 18A-B). (The width at halfheight of the frequency domain sinc centre lobe resulting fromtruncation in the time domain at t_(max) is given (Ernst et al.,Principles of Nuclear Magnetic Resonance in One and Two Dimensions,Clarendon, Oxford (1987), which is hereby incorporated by reference inits entirety) by 0.604/t_(max). In the current implementation of (5,2)DHACACONHN (FIG. 6) all indirect evolution periods except for Ω(¹H^(α))are constant-time periods. The evolution of Ω(¹H^(α)) is implemented ina semiconstant-time manner (Cavanagh et al., Protein NMR Spectroscopy,Academic Press, San Diego (1996), which is hereby incorporated byreference in its entirety), so that signal losses due to transverserelaxation of ¹H^(α) are negligible for 8.6 kDa ubiquitin at shortt_(max) values around 6.5 ms. For larger systems with short T₂(¹H^(α)),however, the semiconstant-time frequency labeling may lead to adetectable increase of ω₁-line widths in the basic when compared tocentral peak spectra.) This yields the same standard deviation ΔΩ forthe identification of peak positions in the two experiments. Hence, thestandard deviation of the chemical shift measurements obtained “after”the least-squares fit is reduced (Eadie et al., Statistical Methods inExperimental Physics, North-Holland, N.Y. (1982), which is herebyincorporated by reference in its entirety) by a factor 1/{squareroot}{square root over (n)} in GFT NMR. For simplicity, it is assumedthat the n peaks which contribute to the calculation of a given shiftexhibit the same line widths (see descriptions of FIGS. 19-20).

[0025] FIGS. 2A-D show a stick diagram exemplifying the formation ofchemical shift multiplets (on the left) for K=3 and phase-sensitivelyedited multiplet components (on the right) in the frequency domain. FIG.2A shows the basic spectra yielding the following linear combinations:B1[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B2[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B3[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B4[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B5[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B6[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B7[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8;B8[Ω₀+Ω₁+Ω₂+Ω₃]=A1+A2+A3+A4+A5+A6+A7+A8. FIG. 2B shows the first ordercentral peak spectra: B9[Ω₀+Ω₁+Ω₂]=A9+A10+A11+A12;B10[Ω₀−Ω₁+Ω₂]=A9−A10+A11−A12; B11[Ω₀+Ω₁−Ω₂]=A9+A10−A11−A12;B12[Ω₀−Ω₁−Ω₂]=A9−A10−A11+A12. FIG. 2C shows the second order centralpeakspectra: B13[Ω₀+Ω₁]=A13+A14; B14[Ω₀−Ω₁]=A13−A14. FIG. 2D shows the thirdorder central peak spectra: B15=A15. For the calculation of the matricesF(K), see Example 1. To facilitate the comparison of the left and theright section the positions of multiplet components are indicated withthin lines.

[0026] FIGS. 3A-B illustrate the “bottom-up” identification of the peaksforming a chemical shift multiplet in GFT NMR, provided that threeindirect dimensions of a FT NMR experiment are jointly sampled (FIG. 1;K=2). FIG. 3A shows that two spin systems exhibiting degenerate chemicalshifts in all other conventionally sampled N_(t)−1 dimensions give riseto basic, first order central and second order central peaks shown inbold (spin system 1) and lighter shade (spin system 2), respectively.Knowledge of the position of the second order central peak of spinsystem 1 allows identification of the corresponding first order centralpeaks of spin system 1. In turn, their knowledge allows unambiguousidentification of the corresponding peaks of spin system 1 in the basicspectra. As indicated by the dashed line on the left in FIG. 3A, thepeaks in B1 and B3 (shown in bold) are centered around the peak in B5(shown in bold), while, as indicated by the dashed line on the right inFIG. 3A, the peaks in B2 and B4 (shown in bold) are centered around thepeak in B5 (shown in bold). This strategy can readily be extended forK>2. In practice, the identification of components belonging to a givenshift multiplets is greatly facilitated by inspection of peakintensities: the components forming a given multiplet are expected toexhibit (nearly) the same intensity. To illustrate this point, theresonance lines of spin system 2 were assumed to be more intense thanthose of spin system 1. FIG. 3B shows that, in addition to chemicalshift degeneracy in the conventionally sampled N_(t)−1 dimensions, thecentral peaks of spin system 1 (as described in FIG. 3A) and those ofspin system 3 (peaks shown in lighter shade) overlap. In this case, thetwo spin systems exhibit degenerate chemical shifts in all but onedimension of an ND FT NMR spectrum. In (N,N_(t))D GFT NMR, the bottom-upidentification of multiplet components resolves and groups the signalsof the two spin systems in the basic spectra, thus yielding theequivalent of the ND chemical shift correlation.

[0027] FIGS. 4A-C illustrate magnetization transfer pathways of thefollowing GFT NMR experiments: (5,2)D HACACONHN and (5,2)D HACA,CONHN(FIG. 4A); (5,3)D HACACONHN and (5,3)D HACA,CO NHN (FIG. 4B); and (4,3)DCBCACONHN and (4,3)D CBCA,CO NHN (FIG. 4C). INEPT-type polarizationtransfers (Cavanagh et al., Protein NMR spectroscopy, Wiley, N.Y.(1996), which is hereby incorporated by reference in its entirety) areindicated by arrows, and Löhr's “en passant” frequency labeling moduleis indicated by a double arrow. The nuclei for which the chemical shiftis detected in quadrature are shown in bold and are underlined. Thenuclei with a grey background are simultaneously sampled in the GFT NMRdimension, and the chemical shifts of the boxed nuclei are used toestablish sequential connectivities. In FIG. 4B, the chemical shifts ofnitrogen spins shown in circles are measured is a separate dimension.

[0028] FIGS. 5A-G illustrate magnetization transfer pathways generatingthe basic spectra of GFT NMR experiments: (i) (4,3)D HNNCACBCA (FIG.5A), (ii) (4,3)D HNN(CO)CACBCA and (4,3)D CBCACA(CO)NHN (FIG. 5B), (iii)(5,3)D HBHACBCACA(CO)NHN (FIG. 5C), (iv) (5,3)D HCC,CH—COSY (FIG. 5D),(v) (5,3)D HBCBCGCDHD (FIG. 5E), (vi) (4,2) HCC,CH—COSY (FIG. 5F), and(vii) (5,2)D HCCCH—COSY (FIG. 5G). In experiments (iv) and (vi), onlymagnetization transfer pathways corresponding to cross peaks in a 4DHCCH—COSY are shown. In experiment (vii), only the magnetizationtransfer pathway corresponding to cross peaks in a relayed 5D HCCCH—COSYis shown. INEPT-type polarization transfer are indicated by doublearrows for “out-and-back” type experiments and single arrows for“out-and-stay” type experiments. The nucleus for which the chemicalshift is detected in quadrature in all spectra constituting the GFT NMRexperiment is underlined. The nuclei with grey background aresimultaneously sampled in a single GFT NMR dimension, and the chemicalshifts of the boxed nuclei are measured in the direct dimension. Thechemical shifts of nitrogen spins (shown in circles) are measured in aseparate dimension in experiments (i), (ii), and (iii), and the chemicalshifts of ¹³C^(δ) and ¹³C_(i) ^(coupled) (shown in circles) are measuredin a separate dimension in experiments (iv) and (v), respectively. Thedouble headed arrows between ¹³C^(α) and ¹³C^(β) in experiments (i),(ii), and (iii) indicate that the chemical shifts of ¹³C^(α/β) [and¹H^(α/β) in (iii)] first evolve independently, prior to transferring to¹³C^(α) for frequency labeling.

[0029]FIG. 6 illustrates the rf pulse sequence used to record the (5,2)DHACACONHN GFT NMR experiment. Rectangular 90° and 180° pulses areindicated by thin and thick vertical bars, respectively, and phases areindicated above the pulses. Where no rf phase is marked, the pulse isapplied along x. The high power 90° pulse lengths were: 5.6 μs for ¹Hand 15.3 μs for ¹³C, and 39 μs for ¹⁵N. Pulses on ¹³C prior to t₁(¹³C)are applied at high power, and ¹³C decoupling during t₁(¹H) is achievedusing a (90_(x)-180_(y)-90_(x)) composite pulse (Ernst et al.,Principles of Nuclear Magnetic Resonance in One and Two Dimensions,Clarendon, Oxford 1987), which is hereby incorporated by reference inits entirety). Subsequently, the 90° and 180° pulse lengths of ¹³C^(α)are adjusted to 51.6 μs and 46 μs, respectively, to minimizeperturbation of the ¹³CO spins (Cavanagh et al., Protein NMRSpectroscopy, Academic Press, San Diego (1996), which is herebyincorporated by reference in its entirety). The width of the 90° pulsesapplied to ¹³CO pulse is 51.6 μs and the corresponding 180° pulses areapplied with same power. A SEDUCE (Cavanagh et al., Protein NMRSpectroscopy, Academic Press, San Diego (1996), which is herebyincorporated by reference in its entirety) 180° pulse with a length 252μs is used to decouple ¹³CO during t₁. WALTZ16 (Ernst et al., Principlesof Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon,Oxford (1987), which is hereby incorporated by reference in itsentirety) is employed to decouple ¹H (rf field strength=9.2 kHz) duringthe heteronuclear magnetization transfers as well as to decouple ¹⁵N(rf=1.78 kHz) during acquisition. The SEDUCE sequence (rf=1.0 kHz) isused for decoupling of ¹³C^(α) during the ¹⁵N chemical shift evolutionperiod. The ¹H rf carrier is placed at 4.78 ppm. The ¹³C^(α), ¹³C′ and¹⁵N rf carriers are set to 56.3 ppm, 174.3 and 119.3 ppm, respectively.The duration and strengths of the pulsed z-field gradients (PFGs) are:G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (1 ms, 24 G/cm); G4 (250μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, 30 G/cm); G7 (500 μs, 8G/cm); G8 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape.The delays are: τ₁=1.6 ms, τ₂=3.6 ms, τ₃=4.4 ms, τ₄=τ₅=24.8 ms, τ₆=5.5ms, τ₇=4.6 ms, τ₈=1 ms. ¹H-frequency labeling is achieved in a semiconstant-time fashion with t₁ ^(a) (0)=1.79 ms, t₁ ^(b) (0)=1 μs, t₁^(c) (0)=1.791 ms, Δt₁ ^(a)=62.5 μs, Δt₁ ^(b)=32.9 μs, Δt₁ ^(c)=29.6 μs.Hence, the fractional increase of the semi constant-time period with t₁equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.53. Phase cycling: φ₀=x; φ₁=x, −x;φ₂=x, x, −x, −x; φ₃=x; φ₄=4x,4(−x); φ₆(receiver)=2(x,−x,−x,x). Thesensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc.114:10663-10665 (1992), which is hereby incorporated by reference in itsentirety, is employed, i.e., the sign of G6 is inverted in concert witha 180° shift of φ₅. In case this enhancement scheme is not employed,quadrature detection is accomplished by altering the phase 4o accordingto States-TPPI (Cavanagh et al., Protein NMR Spectroscopy, AcademicPress, San Diego (1996), which is hereby incorporated by reference inits entirety). For the setting of the phases φ₀, φ₁, φ₂ and φ₃ seeExample 4.

[0030] FIGS. 7A-B depict the experimental scheme for the (5,2)DHACA,CONHN (FIG. 7A) and (4,3)D CBCA,CO NHN GFT NMR (FIG. 7B)experiments. Rectangular 90° and 180° pulses are indicated by filled andopen vertical bars or shaped pulses, respectively, and phases areindicated above the pulses. Where no radio-frequency (rf) phase ismarked, the pulse is applied along x. The high power 90° pulse lengthswere: 5.8 μs for ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. In FIG. 7A,pulses on ¹³C prior to t₁(¹³C) are applied at high power, and ¹³Cdecoupling during t₁(¹H) is achieved using a (90_(x)-180_(y)-90_(x))composite pulse (Cavanagh et al., Protein NMR spectroscopy, Wiley, N.Y.(1996), which is hereby incorporated by reference in its entirety).Subsequently, the 90° and 180° pulse lengths of ¹³C^(α) are adjusted to51.5 μs and 46 μs, respectively, to minimize perturbation of the ¹³COspins. The width of the 90° pulses applied to ¹³CO pulse is 52 μs andthe corresponding 180° pulses are applied with same power. A SEDUCE(Cavanagh et al., Protein NMR spectroscopy, Wiley, N.Y. (1996), which ishereby incorporated by reference in its entirety) 180° pulse with alength 252 μs is used to decouple ¹³CO during t₁(¹³C^(α)). WALTZ16(Cavanagh et al., Protein NMR spectroscopy, Wiley, N.Y. (1996), which ishereby incorporated by reference in its entirety) is employed todecouple ¹H (rf field strength=9.2 kHz) during the heteronuclearmagnetization transfers as well as to decouple ¹⁵N (rf=1.78 kHz) duringacquisition. The SEDUCE sequence (rf=1.0 kHz) is used for decoupling of¹³C^(α) during the ¹⁵N chemical shift evolution period. The ¹H rfcarrier is placed at 4.78 ppm. The ¹³C^(α) and ¹⁵N rf carriers are setto 56.3 ppm and 119.3 ppm, respectively. All ¹³C′ pulses are laminarshifted (Cavanagh et al., Protein NMR spectroscopy, Wiley, N.Y. (1996),which is hereby incorporated by reference in its entirety) by 118 ppmrelative to the ¹³C^(α) carrier position. By setting the spectral widthof the jointly sampled dimension to one half of 118 ppm, the apparentcarrier position for sampling of ¹³C′ chemical shift (174.3 ppm) isfolded on the position of the ¹³C^(α) carrier position at 56.3 ppm. Theduration and strengths of the pulsed z-field gradients (PFGs) are: G₁ (1ms, 24 G/cm); G₂ (100 μs, 16 G/cm); G₃ (1 ms, 24 G/cm); G₅ (1.5 ms, 20G/cm); G₆ (1.25 ms, 30 G/cm); G₇ (500 μs, 8 G/cm); G₈ (125 ms, 29.5G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=1.6ms, τ₂=9.0 ms, τ₄=11.0 ms, τ₅=22.0 ms, τ₆=5.5 ms, τ₇=4.6 ms, τ₈=1 ms.¹H-frequency labeling is achieved in a semi constant-time fashion witht₁ ^(a) (0)=1.7 ms, t₁ ^(b) (0)=1 μs, t₁ ^(c) (0)=1.701 ms, Δt₁ ^(a)=60μs, Δt₁ ^(b)=35.4 μs, Δt₁ ^(c)=−24.6 μs. Hence, the fractional increaseof the semi constant-time period with t₁ equals to λ=1+Δt₁ ^(c)/Δt₁^(a)=0.58. Phase cycling for artefact suppression: φ₀=x; φ₁=x, −x; φ₂=x,x, −x, −x; φ₃=x; φ₄=4x, 4(−x); φ₅=x; φ₆=φ₇=x; φ₈(receiver)=2(x,−x,−x,x).Phases φ₆ and φ₇ are shifted by 500 to compensate for non-resonanceeffects. GFT NMR super phase-cycling for recording the 8 basic spectra:φ₁=x,y; φ₂=2x,2y; φ₃=4x,4y (the G-matrix required for time domainediting is shown in equation 15 in Example 5). For acquisition ofcentral peaks derived from ¹³C steady state magnetization, a second setof data sets with a 180° shift for φ₃ is collected and data are“pre-processed” as described (see equations 13 and 14 in Example 5). Forsecond order central peak detection, the ¹H^(α) and ¹³C^(α) chemicalshift evolution periods are omitted and φ₁=x,y; φ₂=x; φ₃=x. Third ordercentral peaks were detected in 2D [¹⁵N, ¹H]-HSQC (Cavanagh et al.,Protein NMR spectroscopy, Wiley, N.Y. (1996), which is herebyincorporated by reference in its entirety). (The G-matrices required forthe central peak spectra are shown in equations 16-18 in Example 5). Thesensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc.114:10663-10665 (1992), which is hereby incorporated by reference in itsentirety, is employed, i.e., the sign of G6 is inverted in concert witha 180° shift of φ₅. For implementation of (5,3)D HACA,CO NHN, t₁(¹⁵N) isreplaced by t₂(¹⁵N), and quadrature detection in t₁ is accomplished byaltering the phase φ_(I) according to States-TPPI. GFT NMR super phasecycle for the 4 basic spectra: φ₂=x,y; φ₃=2x,2y (the G-matrix requiredfor time domain editing is shown in equation 16 of Example 5). Firstorder central peaks are derived from ¹³C magnetization and are obtainedby acquiring a second set of data sets with a 180° shift for φ₃. Forsecond order central peak detection, t₁(¹H^(α)) and t₁(¹³C^(α)) areomitted. (The G-matrices required for time domain editing of the centralpeak spectra are shown in equations 17 and 18 of Example 5). In FIG. 7B,pulses on ¹³C prior to t₁(¹³C) are applied at high power. Subsequently,the 90° and 180° pulse lengths applied for ¹³C^(α/β) are adjusted to47.5 μs and 42.5 μs, respectively, to minimize perturbation of ¹³COspins. The width of the 90° pulses applied to ¹³CO pulse is 52 μs andthe corresponding 180° pulses are applied with same power. SEDUCE 180°pulses of 200 μs pulse length are used to decouple ¹³CO during t₁ andτ₄. WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz)during the heteronuclear magnetization transfers, as well as to decouple¹⁵N (rf=1.78 kHz) during acquisition. The SEDUCE sequence is used fordecoupling of ¹³C′ during the ¹⁵N chemical shift evolution period(rf=1.0 kHz). The ¹H rf carrier is placed at 4.78 ppm. Initially, the¹³C and ¹⁵N rf carriers are set to 41.3 ppm and 119.3 ppm, respectively.The ¹³C′ carrier position is folded from 174.3 to 41.3 ppm by settingthe spectral width in ω₁ to one half of 133 ppm (=174.3 ppm−41.3 ppm).The ¹³C carrier is set to 56.3 ppm during the τ₇ delay. The duration andstrengths of the pulsed z-field gradients (PFGs) are: G₁ (1 ms, 24G/cm); G₂ (100 μs, 16 G/cm); G₃ (250 μs, 29.5 G/cm); G₄ (250 μs, 30G/cm); G₅ (1.5 ms, 20 G/cm); G₆ (1.25 ms, 30 G/cm); G₇ (500 μs, 8 G/cm);G₈ (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. Thedelays are: τ₀=1.7 ms, τ₁=800 μs, τ₂=2.8 ms, τ₃32 3.3 ms, τ₄=6.6 ms,τ₆=8.8 ms, τ₇=24 ms, τ₈=5.5 ms, τ₀=4.6 ms, τ₁₀=1.0 ms. Phase cycling forartefact suppression: φ₀=x; τ₂=2(x), 2(−x); τ₃=x; τ₄=x, −x;τ₅=τ₆=τ₇=τ₈=x; τ₉(receiver)=x,−x,−x,x. Phases τ₆ and τ₇ are shifted by120° to compensate for non-resonance effects. GFT NMR superphase-cycling for recording the two basic spectra: τ₂=x,y (the G-matrixrequired for time domain editing is shown in equation 17 of Example 5).The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc.114:10663-10665 (1992), which is hereby incorporated by reference in itsentirety, is employed, i.e., the sign of G6 is inverted in concert witha 180° shift of τ₈. Quadrature detection in t₁(¹³C′) is accomplished byaltering the phase τ₆ according to States-TPPI (Cavanagh et al., ProteinNMR spectroscopy, Wiley, N.Y. (1996), which is hereby incorporated byreference in its entirety).

[0031]FIG. 8 depicts the experimental scheme for recording the (4,3)DCBCACO NHN GFT NMR experiment. Rectangular 90° and 180° pulses areindicated by filled and open vertical bars or shaped pulses,respectively, and phases are indicated above the pulses. Where noradio-frequency (rf) phase is marked, the pulse is applied along x. Thehigh power 90° pulse lengths were: 5.8 ,us for ¹H and 15.4 μs for ¹³C,and 38 μs for ¹⁵N. Pulses on ¹³C prior to t₁(¹³C) are applied at highpower. Subsequently, the 90° and 180° pulse lengths applied for¹³C^(α/β) are adjusted to 47.5 μs is and 42.5 μs, respectively, tominimize perturbation of ¹³CO spins. The width of the 90° pulse appliedon ¹³CO pulse is 52 μs and the corresponding 180° pulses are appliedwith same power. A SEDUCE (Cavanagh et al., Protein NMR spectroscopy,Wiley, N.Y. (1996), which is hereby incorporated by reference in itsentirety) 180° pulse with a length of 200 μs is used to decouple ¹³COduring t₁ and τ₄. The length of the spin-lock purge pulses SL_(x) andSL_(y) are 1.2 ms and 0.6 ms, respectively. WALTZ16 (Cavanagh et al.,Protein NMR spectroscopy, Wiley, N.Y. (1996), which is herebyincorporated by reference in its entirety) is employed to decouple ¹H(rf field strength=9.2 kHz) during the heteronuclear magnetizationtransfers as well as to decouple ¹⁵N during acquisition (rf=1.78 kHz)during acquisition. The SEDUCE sequence is used for decoupling of¹³C^(α) during ¹⁵N evolution period (rf=1.0 kHz). The ¹H rf carrier isplaced at the water line at 4.78 ppm. Initially, the ¹³C and ¹⁵N rfcarriers are set to 41.3 ppm and 119.3 ppm, respectively. The ¹³Ccarrier is set to 56 ppm during the second τ₄/2 delay. The ¹³C′ carrierposition is set to 174.3 ppm. The duration and strengths of the pulsedz-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm);G3 (250 μs, 29.5 G/cm); G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6(1.25 ms, 30 G/cm); G7 (500 μs, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFGpulses are of rectangular shape. The delays are: τ₁=800 μs, τ₂=3.1 ms,τ₃=3.6 ms, τ₄32 7.2 ms, τ₅=4.4 ms, τ₆=24.8 ms, τ₇=24.8 ms, τ₈=5.5 ms,τ₉=4.6 ms, τ₁₀=1.0 ms. Phase cycling for artefact suppression: φ₁=x;φ₂=x,x,−x,−x; φ₃=x, −x; φ₄=x, −x; φ₅=−x; φ6=x, x, −x, −x; φ₇=x;φ8(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay etal., J. Am. Chem. Soc. 114:10663-10665 (1992), which is herebyincorporated by reference in its entirety, is employed, i.e., the signof G₆ is inverted in concert with a 180° shift of φ₇ Quadraturedetection in t₁(¹³C′) is accomplished by altering the phase φ₄ accordingto States-TPPI. GFT NMR super phase-cycle for acquisition of the twobasic spectra: φ₂=x,y (the G-matrix required for time domain editing isshown in equation 17 of Example 5). For first order central peakdetection an HNNCO pulse scheme (Cavanagh et al., Protein NMRspectroscopy, Wiley, N.Y. (1996), which is hereby incorporated byreference in its entirety) is employed.

[0032]FIG. 9 depicts the experimental scheme for the (4,3)D HNNCACBCAexperiment. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no radio-frequency (rf) phase is marked, the pulse isapplied along x. The high-power 90° pulse lengths were: 6.0 μs for ¹H,15.0 μs for ¹³C and 42 μs for ¹⁵N. The 90° and 180° pulse lengthsapplied on ¹³C^(α/β) are adjusted to 40 μs and 36 μs, respectively, tominimize perturbation of ¹³CO spins. One lobe sinc pulses of duration 65μs were applied on ¹³CO with null at ¹³C^(α) to decouple ¹³CO from¹³C^(α) spins during t₁ and from ¹⁵N spins during t₂. The selective 90°¹H pulse used to flip back the water magnetization is applied for 1.8 msduration before the first 90° pulse on ¹³C^(α). WALTZ16 is employed todecouple ¹H (rf field strength=9.2 kHz) during the heteronuclearmagnetization transfers as well as to decouple of ¹⁵N (rf=1.78 kHz)during acquisition. The ¹H rf carrier is placed at the position of thesolvent line at 4.78 ppm. The ¹³C^(α) and ¹⁵N carriers are set to 43.0ppm and 120.9 ppm, respectively. The ¹³C carrier is switched to 56 ppmduring the second t₁ delay. The duration and strengths of the pulsedz-field gradients (PFGs) are: G1 (1.0 Ms, 24 G/cm); G2 (100 μs, 16G/cm); G3 (500 μs, 29.5 G/cm); G5 (100 μs, 16 G/cm); G4 (1.5 ms, 20G/cm); G6(1.5 ms, 20 G/cm); G7 (1.25 ms, 30 G/cm); G8 (500 μs, 8 G/cm);G9 (125 μs, 29.5 G/cm). All PFG pulses are of rectangular shape. Arecovery delay of at least 100 μs duration is inserted between a PFGpulse and an rf pulse. The delays have the following values: τ₁=4.6 ms,τ₂=5.4 ms, τ₃=24 ms, τ₄=24 ms, τ₅ =4.8 ms, τ _(c)=7.0 ms. Phase cycling:φ₁=x, −x; φ₂=y; φ₃=x,x, −x, −x; φ₄=x, φ₅=4(x), 4(−x); φ₆=x;φ₇(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay etal., J. Am. Chem. Soc. 114:10663-10665 (1992), which is herebyincorporated by reference in its entirety, is employed, i.e., the signof G7 is inverted in concert with a 180° shift of φ₆. Quadraturedetection in t₁(¹³C^(α)) and t₂(¹⁵N) is accomplished by altering thephases φ₃ and φ₄, respectively, according to States-TPPI. GFT-NMR superphase-cycling for recording the 2 basic spectra are: φ₁=x,y; φ₂=y,x.

[0033]FIG. 10 depicts the experimental scheme for the (4,3)DHNN(CO)CACBCA experiment. Rectangular 90° and 180° pulses are indicatedby thin and thick vertical bars, respectively, and phases are indicatedabove the pulses. Where no radio-frequency (rf) phase is marked, thepulse is applied along x. The high-power 90° pulse lengths were: 6.0 μsfor ¹H, 15.0 μs for ¹³C and 42 μs for ¹⁵N. The 90° and 180° pulselengths applied on ¹³C^(α/β) are adjusted to 40 μs and 36 μs,respectively, to minimize perturbation of ¹³CO spins. One lobe sincpulses of duration 65 μs and with null at ¹³C^(α) were applied on ¹³COto decouple from ¹³C^(α) spins during t₁ and from ¹⁵N spins during t₂.The 90° pulse lengths for the one lobe sinc pulse on ¹³CO was 71 μs. Theselective 90° ¹H pulse used to flip back the water magnetization isapplied for 1.8 ms duration before the first 90° pulse on ¹³C^(α).WALTZ16 is employed to decouple ¹H (rf field strength=9.2 kHz) duringthe heteronuclear magnetization transfers as well as to decouple of ¹⁵N(rf=1.78 kHz) during acquisition. The ¹H rf carrier is placed at theposition of the solvent line at 4.78 ppm. The ¹³C^(α) and ¹⁵N carriersare set to 43 ppm and 120.9 ppm, respectively. The ¹³C carrier isswitched to 56 ppm during the second t₁ delay. The duration andstrengths of the pulsed z-field gradients (PFGs) are: G1 (1.0 ms, 24G/cm); G2 (100 μs, 16 G/cm); G3 (1.0 ms, 29.5 G/cm); G4 (1.5 ms, 20G/cm); G5 (100 μs, 16 G/cm); G6(1.5 ms, 20 G/cm); G7 (1.25 ms, 30 G/cm);G8 (500 Vs, 8 G/cm); G9 (125 μs, 29.5 G/cm). All PFG pulses are ofrectangular shape. A recovery delay of at least 100 μs duration isinserted between a PFG pulse and an rf pulse. The delays have thefollowing values: τ₁=4.4 ms, τ₂=5.4 ms, τ₃=24 ms, τ₄=24 ms, τ₅=4.8 ms,τ_(a)=4.6 ms, τ_(b)=6.8 ms, τ_(c)=6.9 ms. Phase cycling: φ₁=x, −x; φ₂=y;φ₃=x,x, −x, −x; φ₄=x, φ₅=4(x), 4(−x); φ₆=x; φ₇(receiver)=x, −x, −x, x.The sensitivity enhancement scheme of Kay et al., J. Am. Chem. Soc.114:10663-10665 (1992), which is hereby incorporated by reference in itsentirety, is employed, i.e., the sign of G7 is inverted in concert witha 180° shift of φ₆ Quadrature detection in t₁(¹³C) and t₂(¹⁵N) isaccomplished by altering the phases φ₃ and φ₄, respectively, accordingto States-TPPI. GFT-NMR super phase-cycle for recording the 2 basicspectra are: φ₁=x,y; φ₂=y,x.

[0034]FIG. 11 depicts the experimental scheme for the (4,3)DCBCACA(CO)NHN experiment. Rectangular 90° and 180° pulses are indicatedby thin and thick vertical bars, respectively, and phases are indicatedabove the pulses. Where no radio-frequency (rf) phase is marked, thepulse is applied along x. The high-power 90° pulse lengths were: 5.9 μsfor ¹H, 15.4 μs for ¹³C, and 38 μs for ¹⁵N. Pulses on ¹³C prior tot₁(¹³C) are applied at high power, and ¹³C decoupling during t₁(¹H) isachieved using a (90_(x)-180_(y)-90_(x)) composite pulse. Subsequently,the 90° and 180° pulse lengths applied for ¹³C^(α/β) are adjusted to47.5 μs and 42.5 μs, respectively, to minimize perturbation of ¹³COspins. The width of the 90° pulse applied on ¹³CO pulse is 52 μs and thecorresponding 180° pulses are applied with same power. A SEDUCE 180°pulse with a length of 200 μs is used to decouple ¹³CO during t₁ and τ₄.The length of the spin-lock purge pulses SL_(x) and SL_(y) are 1.2 msand 0.6 ms, respectively. WALTZ16 is employed to decouple ¹H (rf fieldstrength=9.2 kHz) during the heteronuclear magnetization transfers aswell as to decouple ¹⁵N during acquisition (rf=1.78 kHz) duringacquisition. The SEDUCE sequence is used for decoupling of ¹³C^(α)during ¹⁵N evolution period (rf=1.0 kHz). The ¹H rf carrier is placed at4.78 ppm. Initially, the ¹³C and ¹⁵N r. f: carriers are set to 43 ppmand 120.9 ppm, respectively. The ¹³C carrier is set to 56 ppm before thefirst τ₄/2 delay period. The duration and strengths of the pulsedz-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm);G3 (250 μs, 29.5 G/cm); G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6(1.25 ms, 30 G/cm); G7 (500 μs, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFGpulses are of rectangular shape. A recovery delay of at least 100 μsduration is inserted between a PFG pulse and an rf pulse. The delaysare: τ₁=600 μs, τ₂=3.1 ms, τ₃=3.35 ms, τ₄=6.8 ms, τ₅=4.4 ms, τ₆=24.6 ms,τ₇=24.6 ms, τ₈=5.5 ms, τ₉=4.6 ms, τ₁₀=1.0 ms. Phase cycling: φ₁=x;φ₂=x,x,−x,−x; φ₃=x, −x; φ₄=x, −x; φ₅=x; φ₆=x, x, −x, −x; φ₇=x; φ₈=x;φ₉(receiver)=x, −x, −x, x. The sensitivity enhancement scheme of Kay etal., J. Am. Chem. Soc. 114:10663-10665 (1992), which is herebyincorporated by reference in its entirety, is employed, i.e., the signof G6 is inverted in concert with a 180° shift of φ₇. GFT-NMR superphase-cycling for recording the 2 basic spectra are: φ₂=x,y. Quadraturedetection in t₁(¹³C) and t₂(¹⁵N) is accomplished by altering the phases48 and 45, respectively, according to States-TPPI.

[0035]FIG. 12 depicts the experimental scheme for the (5,3)DHBHACBCACA(CO)NHN experiment. Rectangular 90° and 180° pulses areindicated by thin and thick vertical bars, respectively, and phases areindicated above the pulses. Where no radio-frequency (rf) phase ismarked, the pulse is applied along x. The scaling factor K, for ¹Hchemical shift evolution during t₁ is set to 1.0. The high-power 90°pulse lengths were: 5.9 μs for ¹H, 15.4 μs for ¹³C, and 38 μs for ¹⁵N.Pulses on ¹³C prior to t₁(¹³C) are applied at high power, and ¹³Cdecoupling during t₁(¹H) is achieved using a (90_(x)-180_(y)-90_(x))composite pulse. Subsequently, the 90° and 180° pulse lengths appliedfor ¹³C^(α/β) are adjusted to 47.5 μs and 42.5 μs, respectively, tominimize perturbation of ¹³CO spins. The width of the 90° pulse appliedon ¹³CO pulse is 52 μs and the corresponding 180° pulses are appliedwith same power. A SEDUCE 180° pulse with a length of 200 μs is used todecouple ¹³CO during t₁ and τ₄. The length of the spin-lock purge pulsesSL_(x) and SL_(y) are 1.2 ms and 0.6 ms, respectively. WALTZ16 isemployed to decouple ¹H (rf field strength=9.2 kHz) during theheteronuclear magnetization transfers as well as to decouple ¹⁵N duringacquisition (rf=1.78 kHz) during acquisition. The SEDUCE sequence isused for decoupling of ¹³C^(α) during ¹⁵N evolution period (rf=1.0 kHz).The ¹H rf carrier is placed at −1 ppm before the start of the semiconstant time ¹H chemical shift evolution period, and then switched tothe water line at 4.78 ppm after the second 90° ¹H pulse. Initially, the¹³C and ¹⁵N r. f. carriers are set to 43 ppm and 120.9 ppm,respectively. The ¹³C carrier is set to 56 ppm during the second τ₄/2delay. The duration and strengths of the pulsed z-field gradients (PFGs)are: G1 (1 ms, 24 G/cm); G2 (100 μs, 16 G/cm); G3 (250 μs, 29.5 G/cm);G4 (250 μs, 30 G/cm); G5 (1.5 ms, 20 G/cm); G6 (1.25 ms, G/cm); G7 (500μms, 8 G/cm); G8 (125 μs, 29.5 G/cm). All PFG pulses are of rectangularshape. A recovery delay of at least 100 μs duration is inserted betweena PFG pulse and an rf pulse. The delays are: τ₁=600 μs, τ₂=3.1 ms,τ₃=3.35 ms, τ₄=6.8 ms, τ₅=4.4 ms, τ₆=24.6 ms, τ₇=24.6 ms, τ₈=5.5 ms,τ₉=4.6 ms, τ₁₀=1.0 ms. ¹H-frequency labeling, at a ¹H resonancefrequency of 600 MHz is achieved in a semi constant-time fashion with t₁^(a) (0)=1.7 ms, t₁ ^(b) (0)=1 μs, t₁ ^(c) (0)=1.701 ms, Δt₁ ^(a)=33.3μs, Δt₁ ^(b)=19.3 μs, Δt₁ ^(c)=−14 μs. Hence, the fractional increase ofthe semi constant-time period with t₁ equals to k=1+Δt₁ ^(c)/Δt₁^(a)=0.58. Phase cycling: φ₁=x; φ₂=x,x,−x,−x; φ₃=x, −x; φ₄=x, −x; φ₅=x;φ₆=x, x, −x, −x; φ₇=x; φ₈=x; φ₉(receiver)=x, −x, −x, x. The sensitivityenhancement scheme of Kay et al., J. Am. Chem. Soc. 114:10663-10665(1992), which is hereby incorporated by reference in its entirety, isemployed, i.e., the sign of G6 is inverted in concert with a 180° shiftof φ₇. Quadrature detection in t₁(¹³C) and t₂(¹⁵N) is accomplished byaltering the phases φ₈ and φ₅, respectively, according to States-TPPI.GFT-NMR super phase-cycling for recording the 4 basic spectra are:φ₁=x,y; φ₂=x,y. For acquisition of central peaks derived from ¹³C steadystate magnetization, a second data set with he shifted by 180°, iscollected.

[0036]FIG. 13 depicts the experimental scheme for the (5,3)D HCC,CH—COSYexperiment. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no radio-frequency (rf) phase is marked, the pulse isapplied along x. The scaling factor κ for ¹H chemical shift evolutionduring t₁ is set to 1.0. The high power 90° pulse lengths were: 5.8 μsfor ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. The lengths of the ¹Hspin-lock purge pulses are: first SL_(x), 2.8 ms; second SL_(x), 1.7 ms;SL_(y): 4.9 ms. SEDUCE is used for decoupling of ¹³CO during t₁ and t₂(rf field strength=1 kHz). WURST is used for decoupling of ¹³C duringacquisition. The ¹H carrier is placed at the position of the solventline at 0 ppm before the start of the first semi constant time ¹Hevolution period, and then switched to the water line at 4.78 ppm afterthe second 90° ¹H pulse. The ¹³C and ¹⁵N rf carriers are set to 43 ppmand 120.9 ppm, respectively. The duration and strengths of the pulsedz-field gradients (PFGs) are: G1 (500 μs, 6 G/cm); G2 (500 μs, 11 G/cm);G3 (100 μs, 12 G/cm); G4 (100 μs, 12.5 G/cm); G5 (4.0 ms, 22 G/cm); G6(500 μs, 5 G/cm); G7 (3.0 ms, 22 G/cm); G8 (400 μs, 6 G/cm). Allgradients are applied along z-axis and are of rectangular shape. All PFGpulses are of rectangular shape. A recovery delay of at least 100 μsduration is inserted between a PFG pulse and an rf pulse. The delaysare: τ₁=1.6 ms, τ₂=750 μs, τ₃=2.65 ms, τ₄=3.4 ms, τ₅=6.8 ms, τ₆=1.6 ms,τ₇=2.4 ms, τ_(a)=350 μs, τ_(b)=1.65 ms and τ_(c)=2.4 ms. Phase cycling:φ₁=x; φ₂=x, −x; φ₃=x, −x; φ₄=x; φ₅=y; φ₆(receiver)=x, −x. Quadraturedetection in t₁(¹³C/¹H) and t₂(¹³C) is accomplished by altering thephases φ₄ and φ₅, respectively, according to States-TPPI. Watersuppression is accomplished by coherence pathway rejection usingspin-lock purge pulses and pulsed field z-gradients. GFT-NMR superphase-cycle for recording the 4 basic spectra are: φ₁=x,y; φ₂=x,y. Foracquisition of central peaks derived from ¹³C steady statemagnetization, a second data set with 4) shifted by 180° is collected.

[0037]FIG. 14 depicts the experimental scheme for the (5,3)D HBCBCGCDHDexperiment. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no radio-frequency (rf) phase is marked, the pulse isapplied along x. The scaling factor K for ¹H chemical shift evolutionduring t₁ is set to 1.0. The high power 90° pulse lengths were: 5.8 μsfor ¹H and 15.4 μs for ¹³C. The first 180° pulse on ¹³C prior to t₁(¹³C)is applied at high power. Subsequently, the 90° pulse lengths of ¹³C^(β)is adjusted to 66 μs. The 180° ¹³C^(β) and ¹³C^(aro) pulses are ofgaussian-3 shape and 375 μs duration. WALTZ16 is used for decoupling of¹H (rf field strength=4.5 kHz) during the magnetization transfer from¹³C^(α) to ¹³C^(aro), and GARP is employed to decouple ¹³C^(aro) (rf=2.5kHz) during acquisition. The ¹H rf carrier is placed at 4.78 ppm. The¹³C rf carrier is set to 38 ppm during ω₀(¹³C) and then switched to 135ppm before the first 90° pulse on ¹³C^(aro) (pulse labeled with φ₄). The¹³C rf carrier is switched back to 125 ppm before the second 90° pulseon ¹³C^(aro). The duration and strengths of the pulsed z-field gradients(PFGs) are: G1 (500 μs, 2 G/cm); G2 (1 ms, 22 G/cm); G3 (2 ms, 10 G/cm);G4 (500 μs, 4 G/cm); G5 (1 ms, −14 G/cm); G6 (500 μs, −2 G/cm). All PFGpulses are of rectangular shape. A recovery delay of at least 100 μsduration is inserted between a PFG pulse and an rf pulse. The delaysare: τ₁=1.8 Ms, τ₂=8.8 ms, τ₃=71 μs, τ₄=4.3 Ms, τ₅=2.1 Ms, τ₆=710 μs,τ₈=1.4 ms, τ₇=2.5 ms. ¹H-frequency labeling, at a ¹H resonance frequencyof 600 MHz is achieved in a semi constant-time fashion with t₁(0)=1.7ms, t₁ ^(b) (0)=1 82 s, t₁ ^(c) (0)=1.701 ms, Δt₁ ^(a)=33.3 μs, Δt₁^(b)=19.3 μs, Δt₁ ^(c)=−14 μs. Hence, the fractional increase of thesemi constant-time period with t₁ equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.58.Phase cycling: φ₁=x; φ₂=x; φ₃=x, y, −x, −y; φ₄=4(x), 4(−x); φ₅=x; φ₆(receiver)=x, −x, x, −x, −x, Quadrature detection in t₁(¹³C^(δ)) andt₂(¹³C^(γ)) is accomplished by altering the phases φ₄ and φ₅,respectively, according to States-TPPI. Water suppression isaccomplished by presaturation of the water line during the relaxationdelay and coherence pathway rejection using spin-lock purge pulses andpulsed field z-gradients. GFT-NMR super phase-cycling for recording the4 basic spectra are: φ₁=x,y; φ₂=x,y. For acquisition of central peaksderived from ¹³C steady state magnetization, a second data set with φ₁shifted by 180° is collected.

[0038]FIG. 15 depicts the experimental scheme for the (4,2)D HCCH—COSYexperiment. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no radio-frequency (rf) phase is marked, the pulse isapplied along x. The high power 90° pulse lengths were: 5.8 μs for ¹Hand 15.4 μs for ¹³C, and 38 μs for ¹⁵N. The lengths of the ¹H spin-lockpurge pulses are: first SL_(x), 2.8 ms; second SL_(x), 1.7 ms; SL_(y):4.9 ms. SEDUCE is used for decoupling of ¹³CO during t₁ and t₂ (rf fieldstrength=1 kHz). WURST is used for decoupling of ¹³C during acquisition.The ¹H carrier is placed at 4.78 ppm. The ¹³C and ¹⁵N rf carriers areset to 43 ppm and 120.9 ppm, respectively. The duration and strengths ofthe pulsed z-field gradients (PFGs) are: G1 (500 is, 6 G/cm); G2 (500is, 11 G/cm); G3 (100 μs, 12 G/cm); G4 (100 μs, 12.5 G/cm); G5 (4 ms, 22G/cm); G6 (500 μs, 5 G/cm); G7 (3 ms, 30 G/cm); G8 (400 μs, 6 G/cm). Allgradients are applied along z-axis and are of rectangular shape. All PFGpulses are of rectangular shape. A recovery delay of at least 100 μsduration is inserted between a PFG pulse and an rf pulse. The delaysare: τ₁=1.6 ms, τ₂=750 μs, τ₃=2.65 ms, τ₄=3.4 ms, τ₅=6.8 ms, τ₆=0.7 ms,τ₇=3.2 ms. Phase cycling: φ₁=x; φ₂=x, −x; φ₃=x, −x; φ₄=x; φ₅=y;φ₆(receiver)=x, −x. Quadrature detection in t₁(¹³C) is accomplished byaltering the phases φ₄ according to States-TPPI. Water suppression isaccomplished by coherence pathway rejection using spin-lock purge pulsesand pulsed field z-gradients. GFT-NMR super phase-cycle for recordingthe 4 basic spectra are: φ₁=x,y; φ₂=x,y. For acquisition of centralpeaks derived from ¹³C steady state magnetization, a second data setwith φ₁ shifted by 180° is collected.

[0039] FIGS. 16A-B show the ω₁[(¹⁵N;¹³C′, ¹³C^(α), ¹H^(α)),ω₂(¹H^(N))]-, [ω₁(¹⁵N;¹³C′, ¹³C^(α)), ω₂(¹H^(N))]-, [ω₁(¹⁵N;¹³C′),ω₂(¹H^(N))]-, and [ω₁(¹⁵N), ω₂(¹H^(N))]-strips taken from the (5,2)DHACACONHN GFT NMR experiment (see FIG. 17). The signals were detected onthe amide proton chemical shift of Ser 20. FIG. 16A shows spectra A1 -A15 containing the chemical shift multiplets. FIG. 16B shows spectraB1-B15 containing the individual edited chemical shift multipletcomponents. Note that when compared with FIG. 2 the order of thechemical shift multiplets appears to have changed. However, this isbecause ω₁(¹H^(α))<0 ppm (i.e., upfield relative to the carrierposition) for Ser 20, and ω₁(¹³C′), ω₁(¹³C^(α)) and ω₁(¹⁵N) >0 ppm (i.e,downfield relative to the respective carrier position). For simplicity,FIG. 2 was designed with the assumption that all resonances are locateddownfield to the respective carrier positions. The signals located athigher field in A15 and B15 arise from a side chain moiety and have thusno corresponding peaks in the other spectra (see also FIG. 17D). Tofacilitate the comparison of FIGS. 16A and 16B, the positions ofmultiplet components are indicated with thin lines.

[0040] FIGS. 17A-E show the 15 2D planes constituting the (5,2)DHACACONHN GFT NMR experiment (K=3) recorded for the 8.6 kDa proteinubiquitin. The linear combination of chemical shifts detected in a givenplane is indicated. FIG. 17A shows the basic spectra B1 to B8. FIG. 17Bshows the first order central peak spectra B9 to B12. FIG. 17C shows thesecond order central peak spectra B13 and B14. FIG. 17D shows the thirdorder central peak spectrum B15. Signals arising from side chainmoieties are in dashed boxes. FIG. 17E shows cross sections taken alongω₁(¹⁵N;¹³C′, ¹³C^(α), ¹H^(α)) at the peak of Ser 20 in B1 (at the top),along ω₁(¹⁵N;¹³C′, ¹³C^(α)) in B9 (second from top), along ω₁(¹⁵N;¹³C′)in B13 (third from top), and along ω₁(¹⁵N) in B15 (at the bottom). Thesections are indicated in green in the corresponding panel. Comparisonof sections from B1 and B9 shows that signals do not broaden withincreasing K (FIG. 18), while the smaller line widths observed inspectra B13 to B15 result from longer t_(max) values (see Example 4).The 15 signals detected on the backbone amide proton of Ile 36 arecircled. Doublets are observed in B1-B8 since Gly 35 exhibitsnon-degenerate ¹H^(α) chemical shifts, yielding the correlation of sixshifts: δ(¹H^(α2))=4.135±0.006 ppm, δ(¹H^(α1))=3.929±0.006 ppm,δ(¹³C^(α))=46.10±0.019 ppm, δ(¹³C′)=173.911±0.017 ppm for Gly 35, andδ(¹⁵N)=120.295±0.043 ppm and δ(¹H^(N))=6.174±0.005 ppm for Ile 36 (Table2). The standard deviations of the indirectly detected chemical shiftswere estimated from a Monte Carlo simulation (see description of FIG.19). In accordance, the ω₂(¹H^(N)) line width of the directly detectedamid proton (20 Hz) was identified with±3σ (99.5% confidence interval)for locating the peak positions. Notably, phase sensitive editing of thechemical shift multiplets yields increasing peak dispersion (and thusresolution) in each of the constituent spectra compared to 2D [¹⁵N,¹H]-HSQC (panel B15). Nearly the same number of peaks is detected ineach of 15 spectra, while the spectral width increases fromSW₁(¹⁵N)=1,440 Hz in B15 to SW₁(¹⁵N/¹³C′/¹³C^(α)/¹H^(α))=8,000 Hz in B1. . . B8.

[0041] FIGS. 18A-C compare line widths and digital resolution of peaksdetected in GFT and FT NMR. FIG. 18A shows (5,2)D HACACONHN GFT NMR:cross sections taken along ω₁(¹⁵N;¹³C′, ¹³C^(α), ¹H^(α)) at the peak ofSer 20 in spectrum B1 (at the top), along ω₁(¹⁵N;¹³C′, ¹³C^(α)) inspectrum B9 (second from top), along ω₁(¹⁵N;¹³C′) in spectrum B13 (thirdfrom top), and along ω₁(¹⁵N) in spectrum B15 (at the bottom). The samet_(max) value was chosen for all spectra in order to demonstrate thatresonances do not broaden when increasing K from 0 to 3. FIG. 18B showsHACACONHN FT NMR: ω₁(¹H^(α)), ω₁(¹³C^(α)), ω₁(¹³C^(α)), and ω₁(¹⁵N)cross sections taken from 2D [ω₁, ω₂(¹H^(N))]- planes obtained with theHACACONHN rf pulse scheme which were (i) recorded with the same t_(max)values and spectral widths, and (ii) were processed as (5,2)D HACACONHN.Comparison of FIG. 18A and FIG. 18B shows that the linewidth registeredin the GFT NMR experiment equals the linewidth in the FT NMR experiment.FIG. 18C shows the same cross sections as in FIG. 18B are shown exceptthat the planes were recorded and processed as a conventional 5D NMRspectrum would be [same maximal evolution times as in the basic spectra,10(t₁)*11(t₂)*22(t₃)*13(t₄)*512(t₅) complex points with spectral widthsof SW₁(¹⁵N)=1,440 Hz, SW₂(¹³C′)=1,500 Hz, SW₃(¹³C^(α))=3,260 Hz, andSW₄(¹H^(α))=1,800 Hz and linear prediction to20(t₁)*22(t₂)*32(t₃)*26(t₄)*512(t₅) complex points]. This would yield afrequency domain data set of 32(ω₁)*32(ω₂)*32(ω3)*32(ω₄)*512((ω₅) realpoints of 2.1 GByte size as compared to 16.8 MByte for (5,2)D HACACONHN.Comparison with FIG. 18B and FIG. 18C makes the relatively poorresolution obtainable in 5D FT NMR apparent. Note that linear predictionand zero filling to ⁹⁶(ω₁)*96(ω₂)*256(ω₃)*128(ω₄)*512(ω₅) real points,which would be the closest match to the digital resolution obtained in(5,2)D HACACONHN, would result in an unrealistically large data size of618 GByte.

[0042]FIG. 19 illustrates Monte-Carlo simulations performed to assessthe increased precision of chemical shift measurements in (5,2)DHACACONHN GFT NMR. Standard deviations for the chemical shiftmeasurements are plotted versus the number of spectra selected from the15 2D spectra constituting this experiment (FIG. 17) in order tocalculate the chemical shifts. σ(¹H^(α)), σ(¹³C^(α)), σ(¹³C′) and σ¹⁵N)represent the deviations for Ω₃(¹H^(α)), Ω₂(¹³C), Ω₁(¹³C′) and Ω₀(¹⁵N)measurements, respectively. The following conservative statistical modelis adopted. Line widths at half height, Δν_(1/2), were measured along Ω₁in (i) B1-B12 (basic spectra and first order central peaks) providingΔν_(1/2)(basic)=Δν_(1/2)(first)=60.1 Hz, (ii) B13 and B14 (second ordercentral peaks) providing Δν_(1/2)(second)=38.2 Hz and (iii) B15 (thirdorder central peaks) providing Δν_(1/2)(3rd)=28.1 Hz [FIG. 17E; thesevalues are close to those expected from the t_(max) values obtainedafter linear prediction]. It is then assumed that the error for theidentification of peak positions is associated with a Gaussiandistribution, and that the Lorenzian line width, Δν_(1/2), represents±3σ (99.5% confidence interval), i.e., Δν_(1/2)=6σ. Δν_(1/2)(basic) isequal to the line widths in the indirect dimensions of conventional FTNMR spectra recorded with the same maximal evolution time (FIGS. 17E and18). Hence, σ(basic) likewise represents the standard deviation obtainedin FT NMR. Correspondingly are c (second)=Δν_(1/2)(second)/6 andσ(third)=Δν_(1/2)(third)/6 the standard deviations for peak positionidentification in B13 and B14, and B15. The deviations σ(¹H^(α)),σ(¹³C^(α)), σ(¹³C′) and σ(¹⁵N) were obtained from Monte Carlosimulations of error propagation for which the following systems ofequations were considered: (i) a minimal number of four out of the eightbasic spectra (B1, B4, B6, B7; FIG. 20) (ii) B1-B8, (iii) B1-B12, (iv)B1-B14, or (v) B1-B15. Peak positions were randomly varied 10,000 timesaccording to Gaussian distributions characterized by σ(basic), σ(second)and σ(third). Subsequently, the systems of equations were solved using aleast-squares fitting routine, and the deviations among the 10,000solutions yielded σ(¹H^(α)), σ(¹³C^(α)), σ(¹³C′) and σ(¹⁵N). Note thatσ(¹H^(α)) is not further reduced when central peaks are involved sincethose do not encode Ω(¹H^(α)). Similarly, σ(¹³C^(α)) and σ(¹³C′) are notfurther reduced when second and third order central peaks are consideredfor calculation of chemical shifts. Notably, the standard deviations(labeled with an asterisk) obtained with four spectra critically dependon the particular selection (FIG. 20). The highest precision is obtainedwhen choosing either B1, B4, B6 and B7, or B2, B3, B5 and B8 (FIGS. 20and 17). The simulations are in neat agreement with calculations usingthe Gaussian law of error propagation (see FIG. 20).

[0043] FIGS. 20A-E show the results of Monte-Carlo simulations for thecase that only four out of eight basic spectra of (5,2)D HACACONHN (FIG.17A) are selected to calculate the chemical shifts. The standarddeviations for the chemical shift measurements are plotted versus thenumber assigned to a particular combination. FIGS. 20A-D show σ(¹⁵N),σ(¹³C′), σ(¹³C) and σ(¹H), respectively, which represent the standarddeviations for the measurement of the chemical shifts Ω₀(¹⁵N), Ω₁(¹³C′),Ω₂(¹³C) and Ω₃(¹H^(α)), respectively. FIG. 20E illustrates theassignment of numbers to the selections of four out of the 64 possiblecombinations $\left\{ {{\begin{pmatrix}8 \\4\end{pmatrix} - 6} = {{{\left( {8 \cdot 7 \cdot 6 \cdot 5} \right)/\left( {4 \cdot 3 \cdot 2 \cdot 1} \right)} - 6} = 64}} \right\}.$

[0044] The six combinations which are subtracted from the binomialcoefficient $\quad\begin{pmatrix}8 \\4\end{pmatrix}$

[0045] correspond to the cases where one of the three chemical shiftsΩ₂, Ω₂₂ or Ω₃ is added to or subtracted from Ω₀ in all of the fourselected spectra (i.e., no splitting is present among the four selectedspectra which encodes the respective chemical shift). The spectraselected for a particular combination number are indicated as dots. Thestatistical model used for the Monte Carlo simulations is the same asdescribed in the legend of FIG. 19.

[0046] FIGS. 21A-B show the composite plot of [ω₁,ω₂]-strips taken from(5,2)D HACA,CONHN (FIG. 21A) and HACACONHN data (FIG. 21B) collected forthe 8.6 kDa protein ubiquitin with a total measurement time of 10.5hours. The 2D data were acquired with 58(t₁):512(t₂) complex points andt_(1max)(¹⁵N; ¹³C′, ¹³C^(α), ¹H^(α))=6.5 ms and t_(2max)(¹H^(N))=73.2ms. In FIG. 21A, the strips were taken from basic spectra (B1 to B8),first order central peak spectra (B9 to B12), second order central peakspectra (B13 and B14) and third order central peak spectra (B15) and arecentered about the amide proton chemical shift of Glu 64. The positionof the backbone ¹⁵N chemical shift of Glu 64 is indicated by a dashedhorizontal line, and the type of linear combination of chemical shiftsdetected for a given strip along ω₁ is indicated at the top of thestrip: B1[Ω₀+Ω₁+Ω₂+Ω₃]; B2[Ω₀−Ω₁+Ω₂+Ω₃]; B3[Ω₀+Ω₁−Ω₂+Ω₃];B4[Ω₀−Ω₁−Ω₂+Ω₃]; B5[Ω₀+Ω₁+Ω₂−Ω₃]; B6[Ω₀−Ω₁+Ω₂−Ω₃]; B7[Ω₀+Ω₁−Ω₂−Ω₃];B8[Ω₀−Ω₁−Ω₂−Ω₃]; B9[Ω₀+Ω₁+Ω₂]; B10[Ω₀−Ω₁+Ω₂]; B11[Ω₀+Ω₁−Ω₂];B12[Ω₀−Ω₁−Ω₂]; B13[Ω₀+Ω₁]; B14[Ω₀−Ω₁]; B15[Ω₀]. In FIG. 21 B, thecorresponding strips are centered about the amide proton chemical shiftof Ser 65. The variation of the 15 peaks relative to the ¹⁵N chemicalshift of Ser 65 (indicated by a dashed horizontal line) matches thevariation about the ¹⁵N chemical shift of Glu 64 in FIG. 21A. Thisallows one to establish the sequential connectivity between Glu 64 andSer 65 based on the measurement of three chemical shifts, i.e.,Ω(¹³C′),Ω(¹³C^(α)) and Ω(¹H^(α)). The shifts are obtained with highprecision (Table 3) since the errors are reduced by the followingfactors when compared with FT NMR. For Ω(¹⁵N): {square root}{square rootover (15)}=3.9; Ω(¹³C′): {square root}{square root over (14)}=3.7;Ω(¹³C^(α)): {square root}{square root over (12)}=3.5; Ω(¹H^(α)): {squareroot}{square root over (8)}=2.8. ¹H and ¹³C chemical shifts are in ppmrelative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0047]FIG. 22 shows the composite plot of [ω₁,ω₃]-strips taken from(5,3)D HACACONHN (strips labeled with ‘a’) and (5,3)D HACA,CONHN data(strips labeled with ‘b’) collected for the 14 kDa NESG consortiumtarget protein TT212 with a total measurement time of 60 hours. The 3Ddata were acquired with 56(t₁):24(t₂):512(t₃) complex points andt_(1max)(¹³C′; ¹³C^(α), ¹H^(α))=6.2 ms, t_(2max)(¹⁵N)=16.4 ms andt_(3max)(¹H^(N))=73.2 ms. The first, second and third pair of strips ineach block has been taken, respectively, at the ¹⁵N chemical shift ofAla 24, Ile 25 and Glu 26 along ω₂(¹⁵N). The strips are centered aboutthe corresponding amide proton shifts detected along ω₃(¹H^(N)). The ¹⁵Nshifts are given at the bottom of each pair of strips, which were takenfrom basic spectra (B1 to B4), the first order central peak spectra (B5and B6) and the second order central peak spectra (B7). The type oflinear combination of chemical shifts detected along ω₁ is indicated atthe top of the strips: B1[Ω₀+Ω₁+Ω₂]; B2[Ω₀−Ω₁+Ω₂]; B3[Ω₀+Ω₁−Ω₂];B4[Ω₀−Ω₁−Ω₂]; B5[Ω₀+Ω₁]; B6[Ω₀−Ω₁]; B7[Ω₀]. Sequential connectivitiesare indicated by horizontal lines and are established based on themeasurement of three chemical shifts, i.e., Ω(¹³C′), Ω(¹³C^(α)), andΩ(¹H^(α)). The chemical shifts were obtained with high precision (Table4), since the errors are reduced by the following factors when comparedwith FT NMR. For Ω(¹³C′): {square root}{square root over (7)}=2.6;Ω(¹³C^(α)): {square root}{square root over (4)}=2.4; Ω(¹H^(α)): {squareroot}{square root over (4)}=2. ¹H and ¹³C chemical shifts are in ppmrelative to 2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0048]FIG. 23 shows the composite plot of [ω₁,ω₃]-strips taken from(4,3)D CBCACONHN (strips labeled with ‘a’) and (4,3)D CBCA,CONHN data(strips labeled with ‘b’) collected for the 8.6 kDa protein ubiquitinwith a total measurement time of 11.2 hours. The 3D data were acquiredwith 60(t₁):24(t₂):512(t₃) complex points and t_(1max)(¹³C′;¹³C^(α/β))=5.9 ms, t_(2max)(¹⁵N)=17.2 ms and t_(3max)(¹H^(N))=73.2 ms.The first, second, and third pair of strips in each block has beentaken, respectively, at the ¹⁵N chemical shift of Glu 64, Ser 65, andThr 66 along ω₂(¹⁵N). The strips are centered about the correspondingamide proton shifts detected along ω₃(¹H^(N)). The ¹⁵N shifts are givenat the bottom of each pair of strips, which were taken from basicspectra (B1 and B2) and the first order central peak spectra (B3). Thetype of linear combination of chemical shifts detected along ω₁ isindicated at the top of the strips: B1[Ω₀+Ω₁]; B2[Ω₀−Ω]; B3[Ω₀].Sequential connectivities are indicated by horizontal lines and areestablished based on the measurement of three chemical shifts, i.e.,Ω(¹³C′),Ω(¹³C^(α)) and Ω(¹³C^(β)). [Since the ¹³C^(α/β) carrier was setin between the ¹³C^(α), and ¹³C^(β)chemical shift ranges (FIG. 7), onehas that peaks at ω₂(¹³C′+¹³C^(α)) and ω₁(¹³C′+¹³C^(β)) in B1 appear ina “reversed order” when compared with B2, which exhibits peaks atω₂(¹³C′−¹³C^(α)) and ω₃(¹³C′−¹³C^(β)).] The chemical shifts wereobtained with high precision (Table 5) since the errors are reduced bythe following factors when compared with FT NMR. For Ω(¹³C′): {squareroot}{square root over (3)}=1.7; Ω(¹³C^(α)): {square root}{square rootover (2)}=1.4; Ω(¹³C^(β)): {square root}{square root over (2)}=1.4. ¹Hand ¹³C chemical shifts are in ppm relative to2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0049]FIG. 24 shows a composite plot of [ω₁,ω₃]-strips taken from (5,3)DHACACONHN (strips labeled with ‘a’) and (5,3)D HACA,CONHN data (stripslabeled with ‘b’) collected for ubiquitin with a total measurement timeof 20.8 hours. The 3D data were acquired with 56(t₁):24(t₂):512(t₃)complex points and t_(1max)(¹³C′; ¹³C^(α), ¹H^(α))=6.2 ms,t_(2max)(¹⁵N)=17.2 ms and t_(3max)(¹H^(N))=73.2 ms. The first, second,and third pair of strips in each block has been taken, respectively, atthe ¹⁵N chemical shift of Lys 63, Glu 64, and Ser 65 along ω₂(¹⁵N). Thestrips are centered about the corresponding amide proton shifts detectedalong ω₃(¹H^(N)). The ¹⁵N shifts are given at the bottom of each pair ofstrips, which were taken from basic spectra (B1 to B4), the first ordercentral peak spectra (B5 and B6) and the second order central peakspectra (B7). The type of linear combination of chemical shifts detectedalong ω₁ is indicated at the top of the strips: B1[Ω₀+Ω₁+Ω₂];B2[Ω₀−Ω₁+Ω₂]; B3[Ω₀+Ω₁−Ω₂]; B4[Ω₀−Ω₁−Ω₂]; B5[Ω₀+Ω₁]; B6[Ω₀−Ω₁]; B7[Ω₀].Sequential connectivities are indicated by horizontal lines and areestablished based on the measurement of three chemical shifts, i.e.,Ω(¹³C′),(¹³C^(α)) and Ω(¹H^(α)). The chemical shifts were obtained withhigh precision (Table 6), since the errors are reduced by the followingfactors when compared with FT NMR. For Ω(¹³C′):; Ω(¹³C^(α)):;Ω(¹H^(α)):. ¹H and ¹³C chemical shifts are in ppm relative to2,2-dimethyl-2-silapentane-5-sulfonate sodium salt (DSS).

[0050]FIG. 25 shows the composite plot of [ω₁(¹³C^(α); ¹³C^(α/β)),ω₃(¹H^(N))] strips taken from the basic spectra of (a) (4,3)D HNNCACBCA(B1a, B2a) and (b) (4,3)D HNN(CO)CACBCA (B1b, B2b). The [ω₁(¹³C^(α)),ω₃(¹H^(N))] strips taken from 3D HNNCA (B3a) and 4D HNN(CO)CA (B3b)spectra represent the first order central peaks for (4,3)D HNNCACBCA and(4,3)D HNN(CO)CACBCA, respectively. As an example, strips correspondingto Ω₂(¹⁵N) and Ω₃(¹H^(N)) chemical shifts for the residue Glu 73 of the16 kDa protein ER75 are shown. Dashed lines connecting peaks establishsequential connectivities. Peaks labeled 1 to 9 in the figure correspondto the following linear combination of chemical shifts (i≡Glu 73;i−1≡Ala 71):

[0051] 1: Ω₀(¹³C_(i−1) ^(α)+Ω) ₁(¹³C_(i−1) ^(α));

[0052] 2: Ω₀(¹³C_(i) ^(α)+Ω) ₁(¹³C_(i) ^(α))

[0053] 3: Ω₀(¹³C_(i) ^(α)+Ω) ₁(¹³C_(i) ^(α)), Ω₀(¹³C_(i−1) ^(α)+Ω)₁(¹³C_(i−1) ^(α))

[0054] 4: Ω₀(¹³C_(i) ^(α)−Ω) ₁(¹³C_(i) ^(α))

[0055] 5: Ω₀(¹³C_(i−1) ^(α)−Ω) ₁(¹³C_(i−1) ^(α))

[0056] 6: Ω₀(¹³C_(i) ^(α)−Ω) ₁(¹³C_(i) ^(β))

[0057] 7: Ω₀(¹³C_(i−1) ^(α)−Ω) ₁(¹³C_(i−1) ^(β))

[0058] 8: Ω₀(¹³C_(i) ^(α))

[0059] 9: Ω₀(¹³C_(i−1) ^(α))

[0060]FIG. 26 shows the composite plot of [ω₁(¹³C^(α); ¹³C^(α/β)),ω₃(¹H^(N))] strips taken from the basic spectra of (a) (4,3)DCBCACA(CO)NHN (B1a and B2a) and (b) (4,3)D HNNCACBCA (B1b and B2b)illustrating how sequential resonance assignments along the polypeptidechain are obtained. As an example, the sequential walk for residues Val27 to Ile 30 of the 7 kDa protein GR2 is shown. For simplicity, only thesequential connectivities inferred from the basic spectra are shown. Theobserved peak patterns are as described in FIG. 25.

[0061]FIG. 27 shows the composite plot of [ω₁(¹³C^(α); ¹³C^(α/β),¹H^(α/β), ω) ₃(¹H^(N))] strips taken from the basic and first ordercentral peak spectra of (5,3)D HBHACBCACA(CO)NHN (B1a, B2a, B3a andB4a). Note that [ω₁(¹³C^(α); ¹³C^(α/β)), ω₃(¹H^(N))] strips taken fromthe basic spectra of (4,3)D CBCACA(CO)NHN (B5b and B6b) show the samepeak patterns as those observed in the first order central peak spectraof (5,3)D HBHACBCACA(CO)NHN (B5a and B6a). As an example, stripscorresponding to ω₂(¹⁵N) and ω₃(¹H^(N)) chemical shifts for Ile 30 ofGR2 are shown. Peaks labeled 1 to 12 in the figure correspond to thefollowing linear combination of chemical shifts for residue Ile 29:

[0062] 1: Ω₀(¹³C^(α))+Ω₁(¹³C^(α))+Ω₂(¹H^(α))

[0063] 2: Ω₀(¹³C^(α))+Ω₁(¹³C^(β))+Ω₂(¹H^(β))

[0064] 3: Ω₀(¹³C^(α))+Ω₁(¹³C^(α))−Ω₂(¹H^(α))

[0065] 4: Ω₀(¹³C^(α))+Ω₁(¹³C^(β))−Ω₂(¹H^(β))

[0066] 5: Ω₀(¹³C^(α))−Ω₁(¹³C^(β))−Ω₂(¹H^(β))

[0067] 6: Ω₀(¹³C^(α))−Ω₁(¹³C^(α))−Ω₂(¹H^(α))

[0068] 7: Ω₀(¹³C^(α))−Ω₁(¹³C^(β))+Ω₂(¹H^(β))

[0069] 8: Ω₀(¹³C^(α))−Ω₁(¹³C^(α))+Ω₂(¹H^(α))

[0070] 9: Ω₀(¹³C^(α))−Ω₁(¹³C^(β))

[0071] 10: Ω₀(¹³C^(α))−Ω₁(¹³C^(α))

[0072] 11: Ω₀(¹³C^(α))+Ω₁(¹³C^(α))

[0073] 12: Ω₀(¹³C^(α))+Ω₁(¹³C^(β))

[0074]FIG. 28 shows the composite plot of [ω₁(¹³C; ¹³C, ¹H), ω₃(¹H)]strips taken from the basic (B1-B4) and first order central peak (B5 andB6) spectra of (5,3)D HCC,CH—COSY. The [ω₁(¹³C), ω₃(¹H)] strips takenfrom 3D (H)C,CH—COSY (B7) represents the second order central peakspectra of (5,3)D HCC,CH—COSY. As an example, strips corresponding toω₂(¹³C^(α)) and ω₃(¹H^(α)) chemical shifts for residue Ile 30 of GR2 areshown. Peaks shown in rectangular boxes correspond to cross peaks in aconventional 4D HCCH—COSY. Peaks labeled 1 to 13 correspond to thefollowing linear combination of chemical shifts: Corresponding peak typein 4D HCCH-COSY (peaks 1-8) and 3D CCH-COSY (peaks 9-12) 1:Ω₀(¹³C^(α)) + Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) “Diagonal peak” 2: Ω₀(¹³C^(α)) +Ω₁(¹³C^(β)) + Ω₂(¹H^(β)) “Cross peak” 3: Ω₀(¹³C^(α)) + Ω₁(¹³C^(α)) −Ω₂(¹H^(α)) “Diagonal peak” 4: Ω₀(¹³C^(α)) + Ω₁(¹³C^(β)) − Ω₂(¹H^(β))“Cross peak” 5: Ω₀(¹³C^(α)) − Ω₁(¹³C^(β)) + Ω₂(¹H^(β)) “Cross peak” 6:Ω₀(¹³C^(α)) − Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) “Diagonal peak” 7: Ω₀(¹³C^(α)) −Ω₁(¹³C^(β)) − Ω₂(¹H^(β)) “Cross peak” 8: Ω₀(¹³C^(α)) − Ω₁(¹³C^(α)) −Ω₂(¹H^(α)) “Diagonal peak” 9: Ω₀(¹³C^(α)) + Ω₁(¹³C^(α)) “Diagonal peak”10: Ω₀(¹³C^(α)) + Ω₁(¹³C^(β)) “Cross peak” 11: Ω₀(¹³C^(α)) − Ω₁(¹³C^(β))“Cross peak” 12: Ω₀(¹³C^(α)) − Ω₁(¹³C^(α)) “Diagonal peak” 13:Ω₀(¹³C^(α))

[0075]FIG. 29 shows the composite plot of [ω₁(¹³C^(δ); ¹³C^(β), ¹H^(β)),ω₃(¹H^(β))] strips taken from the basic (B1-B4) and first order centralpeak (B5 and B6) spectra of (5,3)D HBCBCGCDHD illustrating how resonanceassignments for aromatic side-chain spins are obtained. The[ω₁(¹³C^(δ);¹³C^(β)), ω₃(¹H^(δ))] strips taken from 3D [¹³C^(δ),¹³C^(γ), H^(δ)]—COSY represent the second order central peak spectra of(5,3)D HBCBCGCDHD. As an example, strips corresponding to ω₁(¹³C^(γ))and ω₃(¹H^(δ)) chemical shifts for His 68 of Ubiquitin are shown. Peakslabeled 1 to 7 correspond to the following linear combination ofchemical shifts:

[0076] 1: Ω₀(¹³C^(δ2))−Ω₁(¹³C^(β))−Ω₂(¹H^(β))

[0077] 2: Ω₀(¹³C^(δ2))−Ω₁(¹³C^(β))+Ω₂(¹H^(β))

[0078] 3: Ω₀(¹³C^(δ2))+Ω₁(¹³C^(β))+Ω₂(¹H^(β))

[0079] 4: Ω₀(¹³C^(δ2))+Ω₁(¹³C^(β))−Ω₂(¹H^(β))

[0080] 5: Ω₀(¹³C^(δ2))−Ω₁(¹³C^(β))

[0081] 6: Ω₀(¹³C^(δ2))+Ω₁(¹³C^(β))

[0082] 7: Ω₀(¹³C^(δ2))

[0083]FIG. 30 shows the composite plot of [ω₁(¹³C; ¹³C, ¹H), Ω₂(¹H)]strips taken from the basic (B1-B4) and first order central peak (B5 andB6) spectra of (4,2)D HCCH—COSY spectra illustrating how resonanceassignments for aromatic side-chain spins are obtained. The [ω₁(¹³C),ω₂(¹H)] strip taken from 2D [¹³C-¹H] HSQC (B7) represents the secondorder central peak spectra for (4,2)D HCCH—COSY. As an example, stripscorresponding to ω₂(H^(ε)) chemical shift for residue Tyr 59 of the 8.6kDa protein Ubiquitin are shown. Peaks shown in rectangular boxescorrespond to cross peaks in the conventional 4D HCCH—COSY. Peakslabeled 1 to 15 correspond to the following linear combination ofchemical shifts: Corresponding peak type in 4D HCCH-COSY (peaks 1-8) and3D CCH-COSY (peaks 9-14) 1: Ω₀(¹³C^(ε)) − Ω₁(¹³C^(δ)) − Ω₂(¹H^(δ))“Cross peak” 2: Ω₀(¹³C^(ε)) − Ω₁(¹³C^(ε)) − Ω₂(¹H^(ε)) “Diagonal peak”3: Ω₀(¹³C^(ε)) − Ω₁(¹³C^(δ)) + Ω₂(¹H^(δ)) “Cross peak” 4: Ω₀(¹³C^(ε)) −Ω₁(¹³C^(ε)) + Ω₂(¹H^(ε)) “Diagonal peak” 5: Ω₀(¹³C^(ε)) + Ω₁(¹³C^(ε)) +Ω₂(¹H^(ε)) “Diagonal peak” 6: Ω₀(¹³C^(ε)) + Ω₁(¹³C^(δ)) + Ω₂(¹H^(δ))“Cross peak” 7: Ω₀(¹³C^(ε)) + Ω₁(¹³C^(ε)) − Ω₂(¹H^(ε)) “Diagonal peak”8: Ω₀(¹³C^(ε)) + Ω₁(¹³C^(δ)) − Ω₂(¹H^(δ)) “Cross peak” 9: Ω₀(¹³C^(ε)) −Ω₁(¹³C^(ζ)) “Cross peak” 10: Ω₀(¹³C^(ε)) − Ω₁(¹³C^(δ)) “Cross peak” 11:Ω₀(¹³C^(ε)) − Ω₁(¹³C^(ε)) “Diagonal peak” 12: Ω₀(¹³C^(ε)) + Ω₁(¹³C^(ε))“Diagonal peak” 13: Ω₀(¹³C^(ε)) + Ω₁(¹³C^(δ)) “Cross peak” 14:Ω₀(¹³C^(ε)) + Ω₁(¹³C^(ζ)) “Cross peak” 15: Ω₀(¹³C^(ε))

DETAILED DESCRIPTION OF THE INVENTION

[0084] The present invention provides an NMR data acquisition schemewhich is based on the phase sensitive joint sampling of the indirectdimensions spanning a subspace of a conventional NMR experiment. Thisallows one to very rapidly obtain high dimensional NMR spectralinformation. Since the phase-sensitive joint sampling yields subspectracontaining “chemical shift multiplets”, alternative data processing isrequired for editing the components of the multiplets. The subspectraare linearly combined using a so-called “G-matrix” and subsequentlyFourier transformed. The chemical shifts are multiply encoded in theresonance lines constituting the shift multiplets. This corresponds toperforming statistically independent multiple measurements, and thechemical shifts can thus be obtained with high precision. To indicatethat a combined G-matrix and FT is employed, the new approach is named“GFT NMR spectroscopy”.

[0085] In GFT NMR spectroscopy, the chemical shift evolution periodsspanning a given multidimensional subspace of an FT NMR experiment are“jointly” sampled (FIG. 1). Thereby, the dimensionality N of an FT NMRspectrum can be adjusted to a given target dimensionality, N_(t), bycombined sampling of K+1 chemical shifts Ω₀, Ω₁, . . . Ω_(K) encoded inK+1 indirect dimensions of the ND FT NMR experiment (K=N−N,). Assumingthat Ω₀ is detected in quadrature (Ernst et al., Principles of NuclearMagnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987),which is hereby incorporated by reference in its entirety) and that thesetting of the phases ø_(j) of the radiofrequency pulses exciting thespins of dimensions (j=1 . . . K) ensures cosine modulation, thetransfer amplitude (Ernst et al., Principles of Nuclear MagneticResonance in One and Two Dimensions, Clarendon, Oxford (1987), which ishereby incorporated by reference in its entirety) of the N_(t)Dexperiment is proportional to$^{\quad {\Omega \quad}_{0}t} \cdot {\prod\limits_{j = 1}^{K}\quad {{\cos \left( {\Omega_{j}t} \right)}.}}$

[0086] The resulting peak centered around Ω₀ contains 2^(K) componentsand is designated a “chemical shift multiplet” (FIG. 2).

[0087] A shift of ø_(j) by 90° yields a sin(Ω_(j)t) instead of acos(Ω_(j)t) modulation, (Ernst et al., Principles of Nuclear MagneticResonance in One and Two Dimensions, Clarendon, Oxford (1987), which ishereby incorporated by reference in its entirety), and 2^(K) N_(t)Dspectra are recorded if all phases Ok are systematically varied between0° and 90° (FIG. 1). In turn, a linear combination of these 2^(K)spectra allows for the editing of the chemical shift multipletcomponents (FIG. 2). For brevity, c_(j)=cos(Ω_(j)·t),s_(j)=sin(Ω_(j)·t), and e^(iΩ) ^(_(j)) ^(t)=e^(i) ^(_(j)) are defined,so that$^{_{j}} = {{c_{j} + {i \cdot s_{j}}} = {\left\lbrack {1i} \right\rbrack \cdot {\begin{bmatrix}c_{j} \\s_{j}\end{bmatrix}.}}}$

[0088] With K=1, one obtains for the time evolution of the two shiftmultiplet components encoding sum and difference of Ω₀ and Ω₁.$\begin{matrix}{{\begin{bmatrix}^{j_{1}} \\^{- _{1}}\end{bmatrix} \otimes ^{j_{0}}} = {^{i_{0}} = \begin{bmatrix}{^{_{1}} \cdot ^{_{1}}} \\{^{- _{1}} \cdot ^{_{0}}}\end{bmatrix}}} \\\left. {= {\begin{bmatrix}{\left\lbrack {1i} \right\rbrack \otimes \left\lbrack {1i} \right\rbrack} \\{\left\lbrack {1 - i} \right\rbrack \otimes \left\lbrack {1i} \right\rbrack}\end{bmatrix} \cdot {\begin{bmatrix}c_{1} \\s_{1}\end{bmatrix} \otimes \begin{bmatrix}c_{0} \\s_{0}\end{bmatrix}}}} \right\rbrack \\\left. {\left. \left. {\left. {= {\begin{bmatrix}{1i} \\{1 - i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}} \right\rbrack \cdot {\begin{bmatrix}c_{1} \\s_{1}\end{bmatrix} \otimes \begin{matrix}c_{0} \\s_{0}\end{matrix}}} \right\rbrack \right\rbrack \quad \begin{matrix}c_{0} \\s_{0}\end{matrix}} \right\rbrack\end{matrix}\quad$

[0089] Accordingly, one obtains with K=2 for three chemical shifts Ω₀,Ω₁, and Ω₂: ${{\begin{bmatrix}^{_{2}} \\^{- _{2}}\end{bmatrix} \otimes \begin{bmatrix}^{_{1}} \\^{- _{1}}\end{bmatrix} \otimes ^{_{o}}} = {\left\lbrack {\begin{bmatrix}{1i} \\{1 - i}\end{bmatrix} \otimes \begin{bmatrix}{1i} \\{1 - i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack} \right\rbrack \cdot \left\lbrack {\begin{bmatrix}c_{2} \\s_{2}\end{bmatrix} \otimes \begin{bmatrix}c_{1} \\s_{1}\end{bmatrix} \otimes \begin{bmatrix}c_{0} \\s_{0}\end{bmatrix}} \right\rbrack}},$

[0090] and, in general, for K+1 chemical shifts Ω₀, Ω₁, . . . Ω_(K):${\begin{bmatrix}^{_{K}} \\^{- _{K}}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}^{_{1}} \\^{- _{1}}\end{bmatrix} \otimes ^{_{o}}} = {\left\lbrack {\begin{bmatrix}{1i} \\{1 - i}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}{1i} \\{1 - i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack} \right\rbrack \cdot \left\lbrack {\begin{bmatrix}c_{K} \\s_{K}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}c_{1} \\s_{1}\end{bmatrix} \otimes \begin{bmatrix}c_{0} \\s_{0}\end{bmatrix}} \right\rbrack}$

[0091] The 2^(K) dimensional complex vector on the left side of theequation is proportional to the vector {circumflex over (T)}_(c)(K)comprising the desired edited spectra with the individual components ofthe chemical shift multiplets, that is,${{\hat{T}}_{c}(K)} \sim {\begin{bmatrix}^{_{K}} \\^{- _{K}}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}^{_{1}} \\^{- _{1}}\end{bmatrix} \otimes ^{_{o}}}$

[0092] The 2^(K+1) dimensional real vector of the 2^(K+1) trigonometricmodulations on the right side of the equation is proportional to thevector containing the spectra with the chemical shift multiplets in thereal, Sjr, and imaginary parts, Sji, of the 2^(K) N_(t)D spectra (J=1 .. . 2^(K)). Hence, with Ŝ(K)=[S_(1r)S_(1i)S_(2r)S_(2i) . . . S₂ ^(K)_(r)S₂ ^(K) _(i)]^(T), ${\hat{S}(K)} \sim {\begin{bmatrix}c_{K} \\s_{K}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}c_{1} \\s_{1}\end{bmatrix} \otimes \begin{bmatrix}c_{0} \\s_{0}\end{bmatrix}}$

[0093] For the 2^(K)×2^(K+1) complex G-matrix, which transforms Ŝ(K)into {circumflex over (T)}(K) according to the following equation (1):

{circumflex over (T)} _(c)(K)=Ĝ _(c)(K)·Ŝ(K)  (1)

[0094] one then obtains ${G_{c}(K)} = \left\lbrack {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \quad \ldots \quad \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1\quad i} \right\rbrack} \right\rbrack$

[0095] Alternatively, the multiplet components may be edited in thefrequency domain (FIG. 2). The spectra of Ŝ(K) are Fourier transformedand a zero-order phase correction of n·90° is applied, depending on thenumber n of chemical shift sine modulations (see Example 1). Theresulting real parts contain purely absorptive chemical shift multipletsand form the 2^(K) dimensional real vector Â(K). Their linearcombination yields the edited spectra contained in the 2^(K) dimensionalreal vector according to the following equation (2):

{circumflex over (B)}(K)={circumflex over (F)}(K)·{circumflex over(A)}(K)  (2)

[0096] Hence, {circumflex over (B)}(K) represents spectra which containthe edited 2^(K) individual multiplet components at Ω₀±Ω₁± . . . Ω_(K)encoding the desired K+1 chemical shifts. {circumflex over (F)}(K) canbe readily obtained from {circumflex over (F)}(K−1) by tensor productformation using the relation {circumflex over (F)}(K)={circumflex over(F)}=(K−1){circle over (X)}{circumflex over (F)}(1), with${F(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$

[0097] for details and the relation between F and the G-matrix seeExample 1).

[0098] The 2^(K) spectra of {circumflex over (T)}_(c)(K) and {circumflexover (B)}(K) are designated “basic spectra”. Additional information isrequired to unambiguously derive all shift correlations of the parent NDexperiment (which resolves degeneracy in up to N−1 dimensions) if twomultiplets exhibit degenerate chemical shifts in all of the“conventionally” sampled N_(t)−1 dimensions. The acquisition of peaksdefining the centers of the chemical shift splittings (“central peaks”)at the frequencies Ω₀+Ω₁± . . . ±Ω_(K−1), Ω₀±Ω₁± . . . Ω_(K−2), . . . ,Ω₀±Ω₁, and Ω₀ is then needed for identifying the components forming agiven multiplet (FIG. 3A). Such “central peak acquisition” has beenintroduced in the framework of the reduced-dimensionality NMR approach(Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002);Szyperski et al. J. Biomol. NMR. 3:127-132 (1993); Szyperski et al., J.Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B105:188-191 (1994); Brutscher et al., J. Magn. Reson. B 105:77-82(1994); Szyperski et al., J. Magn. Reson. B 108:197-203 (1995);Brutscher et al., J. Magn. Reson. B 109:238-242 (1995); Szyperski etal., J. Am. Chem. Soc. 118:8146-8147 (1996); Bracken et al., J. Biomol.NMR 9:94-100 (1997); Szyperski et al., J. Biomol NMR, 11:387-405 (1998);Astrof et al., J. Magn. Reson. 152:303-307 (2001); Xia et al., J.Biomol. NMR 24:41-40 (2002), which are hereby incorporated by referencein their entirety). The shift correlations of the ND spectrum can beobtained by “bottom-up” identification of the shift multiplets. Thisprocedure essentially groups the peaks of the basic spectra into setseach belonging to one multiplet (FIG. 3). Because the basic peaks of twospin systems can be grouped even if central peaks overlap (FIG. 3B),this approach ensures that all correlations of the ND experiment areretained. GFT NMR (FIG. 1) thus requires one to record a total of$p = {{\sum\limits_{k = 0}^{K}\quad 2^{k}} = {2^{K + 1} - 1}}$

[0099] N_(t)D spectra, including 2^(K) basic spectra and 2^(K)−1 centralpeak spectra. The p data sets constitute an “(N,N_(t))D GFT NMRexperiment”, and central peaks arising from omission of m chemicalshifts are denoted to be of m-th order. For practical purposes, it isimportant to note that all components of a given multiplet have quitesimilar intensities since they are generated by multiple sine or cosinemodulation of the transfer amplitude. Usually this does not hold for twopeaks belonging to two different spin systems (FIG. 3A), because thenuclear spin relaxation times determining the peak intensities vary fromspin system to spin system. Hence, inspection of peak intensitiesgreatly facilitates the grouping of the peaks.

[0100] The joint sampling of several indirect dimensions reduces theminimal measurement time, T_(m), of an (N,N_(t))D GFT NMR experimentwhen compared with the parent ND FT experiment. The K+1 dimensions of anFT NMR spectrum exhibiting the spectral widths SW₀, SW₁, . . . , SW_(K)are sampled with n₀, n₁, . . . n_(K) complex points and yield maximalevolution times of t_(0,max), t_(1,max), . . . t_(K,max). In the(N,N_(t))D GFT NMR experiment, the same maximal evolution times of theparent ND experiment can be realized by appropriate scaling ofincrements. (Szyperski et al. J. Biomol. NMR. 3:127-132 (1993);Szyperski et al., J. Magn. Reson. B 105:188-191 (1994), which are herebyincorporated by reference in their entirety). The acquisition of bothcosine and sine modulated spectra for all jointly sampled chemicalshifts (equation 1) corresponds to their phase-sensitive acquisition(Brutscher et al., J. Magn. Reson. B 109:238-242 (1995), which is herebyincorporated by reference in its entirety) and allows one to place therf carrier positions in the center of the spectral ranges. Hence, thespectral width required for combined sampling is given by${{SW} = {\sum\limits_{j = 0}^{K}\quad {\kappa_{j} \cdot {SW}_{j}}}},$

[0101] SW_(j), where κ_(j) represents the factor to scale (Szyperski etal. J. Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn.Reson. B 105:188-191 (1994), which are hereby incorporated by referencein their entirety) the sampling increments of the jth dimension toadjust maximal evolution times. If the same maximal evolution time ischosen for all dimensions and assuming, for simplicity, that delayedacquisition starts${{at}\quad {1/{SW}_{j}}},{n = {\sum\limits_{j = 0}^{K}\quad n_{j}}}$

[0102] complex points are required to sample the resulting singledimension [if acquisition starts at t=0, one obtains that$\left. {n = {\left( {\sum\limits_{j = 0}^{K}\quad n_{j}} \right) - K}} \right\rbrack.$

[0103] The ratio ε of the minimal measurement time of an FT NMRexperiment, T_(m)(FT), and the corresponding GFT NMR experiment,T_(m)(GFT), is then given by the number of FIDs that are required tosample the K+1 FT NMR dimensions divided by p times the number of FIDsrequired to sample the resulting single dimension: $\begin{matrix}{ɛ = {\frac{T_{m}({FT})}{T_{m}({GFT})} = {\left( {2^{K}/\left( {2^{K + 1} - 1} \right)} \right) \cdot {\left( {\prod\limits_{j = 0}^{K}\quad n_{j}} \right)/\left( {\sum\limits_{j = 0}^{K}\quad n_{j}} \right)}}}} & (3)\end{matrix}$

[0104] This ratio scales with the product of the number of points overthe corresponding sum and, thus, predicts large reductions in T_(m) (seeTable 1 in Example 3; different ways to implement central peakacquisition as well as the impact of a particular implementation on εare described in Examples 2 and 3). (The GFT NMR scheme can begeneralized by its M-fold application. Since this would involve Mdifferent G-matrices, such an experiment could be designated a G^(M)FTNMR experiment. For example, two groups of dimensions can be identifiedwith each group being combined to a single dimension. First an (N,N′)Dexperiment is devised in which dimensions 1,2 . . . i are jointlysampled. Subsequently, the dimensionality of this experiment is toreduced to an (N,N_(t)) experiment by jointly sampling dimensions i+1,i+2, . . . K+2. For M projection steps, each invoking different sets ofdimensions combined to a single one, the total reduction in minimalmeasurement time is then given by${ɛ^{tot} = {\prod\limits_{j = 1}^{M}\quad ɛ_{j}}},$

[0105] where ε_(j) is the reduction due to the j-th projection (equation3)). The S/N of each of the 2^(K) components in the basic spectra isreduced by (1/{square root}{square root over (2)})^(K) compared to thesingle peak in FT NMR. This is because each chemical shift splittingreduces the S/N by a factor of 2 relative to the FT NMR spectrum, whilea factor of {square root}{square root over (2)} is gained, becausefrequency discrimination is not associated with a FT (see FIG. 2: bothcosine and sine modulated parts contribute equally to the signalintensity in the edited spectra) (The S/N ratio of FT NMR can berecovered by symmetrization about central peaks as described forreduced-dimensionality NMR (Szyperski et al., J. Magn. Reson. B108:197-203 (1995), which is hereby incorporated by reference in itsentirety) using the “bottom up” strategy employed for identification ofshift multiplets (FIG. 3). Note that a reduced sensitivity is notrelevant in the sampling limited regime.)

[0106] GFT NMR spectroscopy combines (i) multiple phase sensitive RDNMR, (ii) multiple ‘bottom-up’ central peak detection, and (iii) (timedomain) editing of the components of the chemical shift multiplets. Theresulting formalism embodies a flexible, generally applicable NMR dataacquisition scheme. Provided that m=K+1 chemical shift evolution periodsof an ND experiments are jointly sampled in a single indirect “GFTdimension”, p=2^(m)−1 different (N−K)D spectra represent the GFT NMRexperiment containing the information of the parent ND experiment.Hence, such a set of p spectra is named an (N,N−K)D GFT NMR experiment.

[0107] Thus, the present invention relates to a method of conducting a(N,N−K) dimensional (D) G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment, where N is the dimensionality of anN-dimensional (ND) Fourier transformation (FT) NMR experiment and K isthe desired reduction in dimensionality relative to N. The methodinvolves providing a sample and applying radiofrequency pulses for theND FT NMR experiment to the sample. Then, m indirect chemical shiftevolution periods of the ND FT NMR experiment are selected, where mequals K+1, and the m indirect chemical shift evolution periods arejointly sampled. Next, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate (N−K)D basic NMRspectra containing frequency domain signals with 2^(K) chemical shiftmultiplet components, thereby enabling phase-sensitive sampling of alljointly sampled m indirect chemical shift evolution periods. Finally,the (N−K) D basic NMR spectra are transformed into (N−K) Dphase-sensitively edited basic NMR spectra, where the 2^(K) chemicalshift multiplet components of the (N−K) D basic NMR spectra are editedto yield (N−K) D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

[0108] As described earlier, the (N−K) D basic NMR spectra can betransformed into (N−K) D phase-sensitively edited basic NMR spectra byapplying a G-matrix defined as${{\hat{G}(K)} = \left\lbrack {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \quad \ldots \quad \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1\quad i} \right\rbrack} \right\rbrack},$

[0109] where i={square root}{square root over (−1)}, under conditionseffective to edit the chemical shift multiplet components in the timedomain. Alternatively, the transforming can be carried out by applying aF-matrix defined as {circumflex over (F)}(K)={circumflex over(F)}(K−1){circle over (X)}{circumflex over (F)}(1), where${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$

[0110] under conditions effective to edit the chemical shift multipletcomponents in the frequency domain.

[0111] In an alternate embodiment, the method of conducting a (N,N−K)DGFT NMR experiment can further involve selecting m′ indirect chemicalshift evolution periods of the (N−K)D FT NMR experiment, where m′ equalsK′+1. Then, the m′ indirect chemical shift evolution periods are jointlysampled. Next, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate (N−K−K′)D basic NMRspectra containing frequency domain signals with 2^(K′) chemical shiftmultiplet components, thereby enabling phase-sensitive sampling of alljointly sampled m′ indirect chemical shift evolution periods. Finally,the (N−K−K′) D basic NMR spectra are transformed into (N−K−K′) Dphase-sensitively edited basic NMR spectra, wherein the 2^(K′) chemicalshift multiplet components of the (N−K−K′) D basic NMR spectra areedited to yield (N−K−K′) D phase-sensitively edited basic NMR spectrahaving individual chemical shift multiplet components. Theabove-mentioned steps of selecting, jointly sampling, independentlycosine and sine modulating, and transforming can be repeated one or moretimes, where m′ is modified for each repetition.

[0112] In an alternate embodiment, the method of conducting a (N,N−K)DGFT NMR experiment can further involve repeating one or more times thesteps of selecting, jointly sampling, independently cosine and sinemodulating, and transforming, where, for each repetition, the selectinginvolves selecting m-j indirect chemical shift evolution periods out ofthe m indirect chemical shift evolution periods, wherein j ranges from 1to K, under conditions effective to generate 2^(K-j) jth order centralpeak NMR spectra.

[0113] The method of conducting a (N,N−K)D GFT NMR experiment can alsoinvolve applying radiofrequency pulses of N-dimensional nuclearOverhauser enhancement spectroscopy (NOESY) (Ernst et al., Principles ofNuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford(1987), which is hereby incorporated by reference in its entirety).Alternatively, the method can involve applying radiofrequency pulses ofN-dimensional transverse relaxation optimized spectroscopy (TROSY)(Pervushin et al., Proc. Natl. Acad. Sci. USA, 94:12366-12371 (1997),which is hereby incorporated by reference in its entirety). In addition,the method can involve applying radiofrequency pulses so that spin-spincouplings are measured (Ernst et al., Principles of Nuclear MagneticResonance in One and Two Dimensions, Clarendon, Oxford (1987), which ishereby incorporated by reference in its entirety). The spin-spincouplings can be residual dipolar spin-spin coupling constants (Bax,Protein Sci., 12:1-16 (2003), which is hereby incorporated by referencein its entirety). The method can also involve applying radiofrequencypulses so that nuclear spin relaxation times are measured by samplingnuclear spin relaxation delays (Palmer, Annu. Rev. Biophys. Biomol.Struct., 30:129-155 (2001), which is hereby incorporated by reference inits entirety). The spin relaxation delays can be further jointly sampledwith chemical shift evolution periods (Ernst et al., Principles ofNuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford(1987), which is hereby incorporated by reference in its entirety). Inanother embodiment, the jointly sampling the m indirect chemical shiftevolution periods is achieved with a single continuous acquisition(Frydman et al., Proc. Natl. Acad. Sci., U.S.A., 99:15858-15862 (2002),which is hereby incorporated by reference in its entirety).

[0114] The present invention also discloses specific GFT NMR experimentsand different combinations of those experiments which allows one toobtain sequential backbone chemical shift assignments for determiningthe secondary structure of a protein molecule and complete assignmentsof chemical shift values for a protein molecule including aliphatic andaromatic sidechain spin systems.

[0115] Specific GFT NMR Experiments

[0116] The present invention discloses the following six (N,N−K)D GFTNMR experiments for the assignment of polypeptide backbone and ¹³C^(β)resonance: (i) with K=3, (5,2)D [HACACONHN] GFT NMR experiment and(5,2)D [HACA,CONHN] GFT NMR experiment for sequential assignment, (ii)with K=2, (5,3)D [HACA,CONHN GFT NMR experiment and (5,3)D [HACACONHN]GFT NMR experiment, where, in contrast to the (5,2)D experiments in (i),the ¹⁵N chemical shifts evolve separately, and (iii) with K=1, (4,3)D[CBCACONHN] GFT NMR experiment and (4,3)D [CBCA,CONHN] GFT NMR. Theunderlined letters indicate which chemical shifts that are jointlysampled. After G-matrix transformation, one obtains 2³⁺¹−1=15 2D planesfor the (5,2)D experiments (K=3), seven 3D spectra for the (5,3)Dexperiments (K=2) and three 3D spectra for the (4,3)D experiments (K=1).FIG. 4 illustrates the magnetization transfer pathways of the specificembodiments of these six GFT NMR experiments. (5,2)D [HACA,CONHN]/(5,2)D[HACACONHN] GFT NMR experiments and (5,3)D [HACA,CONH]/(5,3)D[HACACONHN] GFT NMR experiments correlate the backbone amide ¹⁵N and ¹HNchemical shifts of residue i with the ¹³C′, ¹³C^(α) and ¹H^(α) chemicalshifts of residue i−1 and i, respectively, via one-bond scalar couplings(FIGS. 4A-B). In addition, the often smaller two-bond scalar couplingsbetween the ¹⁵N_(i) and ¹³C^(α) _(i−1), may yield sequentialconnectivities in the HACA,CONHN experiments. The comma separating “CA”from “CO” indicates that the intraresidue ¹³C′ chemical shift isobtained by creating two-spin coherence involving ¹³C′ and ¹³C′ duringthe intraresidue polarization transfer from ¹³C^(α) to ¹⁵N (Löhr et al.,J. Biomol. NMR 6:189-197 (1995), which is hereby incorporated byreference in its reference). (4,3)D [CBCACONHN] and (4,3)D [CBCA,CONHN]GFT NMR experiments correlate the backbone amide ¹⁵N and ¹HN chemicalshifts of residue i with the ¹³C′, ¹³C^(α) and ¹³C^(β) chemical shiftsof residue i−1 and i, respectively, via one-bond scalar couplings (FIG.4C), and the often smaller two-bond scalar couplings between the ¹⁵N_(i)and ¹³C^(α) _(i−1) may yield additional sequential connectivities in(4,3)D [CBCA,CONHN].

[0117] Thus, the present invention relates to the above method ofconducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals3 to conduct a (5,2)D [HACACONHN] GFT NMR experiment. In this method,(a) the sample is a protein molecule having two consecutive amino acidresidues, i−1 and i, and the chemical shift values for the followingnuclei are measured: (1) an α-proton of amino acid residue i−1, ¹H^(α)_(i−1); (2) an α-carbon of amino acid residue i−1, ¹³C^(α) _(i−1); (3) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1); (4) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (5) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(I), (b) the selecting involves selecting 4chemical shift evolution periods of the 5D FT NMR experiment, ¹H^(α)_(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i), and (c) the jointlysampling involves jointly sampling the 4 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α)_(i−1), ¹³C′_(i−1), ¹⁵N_(i)). One specific embodiment of this method((5,2)D HACACONHN) involves applying radiofrequency pulses for a 5D FTNMR experiment according to the scheme shown in FIG. 6.

[0118] The present invention also relates to the above method ofconducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals3 to conduct a (5,2)D [HACA,CONHN] GFT NMR experiment. In this method,(a) the sample is a protein molecule having an amino acid residue, i,and the chemical shift values for the following nuclei are measured: (1)an α-proton of amino acid residue i−1, ¹H^(α) _(i−1); (2) an α-carbon ofamino acid residue i−1, ¹³C^(α) _(i−1); (3) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) a polypeptidebackbone amide nitrogen of amino acid residue i−1, ¹⁵N_(i−1); and (5) apolypeptide backbone amide proton of amino acid residue i−1, ¹H^(N)_(i−1), (b) the selecting involves selecting 4 chemical shift evolutionperiods of the 5D FT NMR experiment, ¹H^(α) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1), and ¹⁵N_(i−1), and (c) the jointly sampling involves jointlysampling the 4 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1),¹⁵N_(i−1)). One specific embodiment of this method ((5,2)D HACA,CONHN)involves applying radiofrequency pulses for a 5D FT NMR experimentaccording to the scheme shown in FIG. 7A.

[0119] Another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 andK equals 2 to conduct a (5,3)D [HACACONHN] GFT NMR experiment. In thismethod, (a) the sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) an α-proton of amino acid residuei−1, ¹H^(α) _(i−1); (2) an α-carbon of amino acid residue i−1, ¹³C^(α)_(i−1); (3) a polypeptide backbone carbonyl carbon of amino acid residuei−1, ¹³C′_(i−1); (4) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (5) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹H^(α)_(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1), and (c) the jointly samplinginvolves jointly sampling the 3 chemical shift evolution periods in anindirect time domain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1)).

[0120] Yet another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 andK equals 2 to conduct a (5,3)D [HACA,CONHN] GFT NMR experiment. In thismethod, (a) the sample is a protein molecule having an amino acidresidue, i−1, and the chemical shift values for the following nuclei aremeasured: (1) an α-proton of amino acid residue i−1, ¹H^(α) _(i−1); (2)an α-carbon of amino acid residue i−1, ¹³C^(α) _(i−1); (3) a polypeptidebackbone carbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) apolypeptide backbone amide nitrogen of amino acid residue i−1,¹⁵N_(i−1); and (5) a polypeptide backbone amide proton of amino acidresidue i−1, ¹H^(N) _(i), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹H^(α)_(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1), and (c) the jointly samplinginvolves jointly sampling the 3 chemical shift evolution periods in anindirect time domain dimension, t₁(¹ H^(α) _(i−1,) ¹³C^(α) _(i−1),¹³C′_(i−1)).

[0121] A further aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 andK equals 1 to conduct a (4,3)D [CBCACONHN] GFT NMR experiment. In thismethod, (a) the sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i−1); (2) a polypeptide backbone carbonylcarbon of amino acid residue i−1, ¹³C′_(i−1); (3) a polypeptide backboneamide nitrogen of amino acid residue i, ¹⁵N_(i); and (4) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i), (b) theselecting involves selecting 2 chemical shift evolution periods of the4D FT NMR experiment, ¹³C^(α/β) _(i−1) and ¹³C′_(i−1) ₁ and (c) thejointly sampling involves jointly sampling the 2 chemical shiftevolution periods in an indirect time domain dimension, t₁(¹³C^(α/β)_(i−1), ¹³C′_(i−1)). One specific embodiment of this method ((4,3)DCBCACONHN) involves applying radiofrequency pulses for a 4D FT NMRexperiment according to the scheme shown in FIG. 8.

[0122] The present invention also relates to the above method ofconducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals1 to conduct a (4,3)D [CBCA,CONHN] GFT NMR experiment. In this method,(a) the sample is a protein molecule having an amino acid residue, i−1,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1); (3) a polypeptide backbone amide nitrogen of amino acidresidue i−1, ¹⁵N_(i−1); and (4) a polypeptide backbone amide proton ofamino acid residue i−1, ¹H^(N) _(i−1), (b) the selecting involvesselecting 2 chemical shift evolution periods of the 4D FT NMRexperiment, ¹³C^(α/β) _(i−1) and ¹³C′_(i−1), and (c) the jointlysampling involves jointly sampling the 2 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹³C^(α/β) _(i−1),¹³C′_(i−1)). One specific embodiment of this method ((4,3)D CBCA,CONHN)involves applying radiofrequency pulses for a 4D FT NMR experimentaccording to the scheme shown in FIG. 7B.

[0123] In addition, the present invention discloses the following GFTNMR experiments for the assignment of polypeptide backbone and sidechainresonances: (i) (4,3)D [HNNCACBCA] GFT NMR experiment, (ii) (4,3)D[CBCACA(CO)NHN]/(4,3)D [HNN(CO)CACBCA] GFT NMR experiments, (iii) (5,3)D[HBHACBCACA(CO)NHN] GFT NMR experiment, (iv) (5,3)D [HCC,CH—COSY] GFTNMR experiment, (v) (5,3)D [HBCBCGCDHD] GFT NMR experiment, (vi) (4,2)D[HCCH—COSY] GFT NMR experiment, and (vii) (5,2)D [HCCCH—COSY] GFT NMRexperiment. Experiment (i) and (ii)/(iii) form pairs to sequentiallyassign backbone ¹³C^(α) and ¹³C^(β) resonances. Experiment (iii) alsoprovides ¹H^(α/β) chemical shifts. The ¹³C^(α/β) and ¹H^(α/β) chemicalshifts, in turn, allow one to assign more peripheral spins of thealiphatic side-chain of a given amino acid residue using experiment(iv). Experiments (v) and (vi) can be used for resonance assignments ofaromatic side-chain spins. The assignment of the side-chain chemicalshifts can be further supported with experiment (vii). The magnetizationtransfer pathways of specific embodiments of these GFT NMR experiments(i)-(vii) are depicted in FIGS. 5A-G, respectively.

[0124] Thus, the present invention also relates to the above method ofconducting a (N,N−K)D GFT NMR experiment, where N equals 4 and K equals1 to conduct a (4,3)D [HNNCACBCA] GFT NMR experiment. In this method,(a) the sample is a protein molecule having two consecutive amino acidresidues, i−1 and i, and the chemical shift values for the followingnuclei are measured: (1) α- and β-carbons of amino acid residues i andi−1, ¹³C^(α/β) _(i/i−1); (2) a polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i); and (3) a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i), (b) the selecting involvesselecting 2 chemical shift evolution periods of the 4D FT NMRexperiment, ¹³C^(α/β) _(i/i−1) and ¹³C^(α) _(i/i−1), and (c) the jointlysampling involves jointly sampling the 2 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹³C^(α/β) _(i/i−1),¹³C^(α) _(i/i−1)). One specific embodiment of this method ((4,3)DHNNCACBCA) involves applying radiofrequency pulses for a 4D FT NMRexperiment according to the scheme shown in FIG. 9.

[0125] In an alternate embodiment, the above method can be modified,where N equals 4 and K equals 2, to conduct a (4,2)D [HNNCACBCA] GFT NMRexperiment. In this method, (a) the sample is a protein molecule havingtwo consecutive amino acid residues, i−1 and i, and the chemical shiftvalues for the following nuclei are measured: (1) α- and β-carbons ofamino acid residues i and i−1, ¹³C^(α/β) _(i/i−1); (2) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (3) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i),(b) the selecting involves selecting 3 chemical shift evolution periodsof the 4D FT NMR experiment, ¹³C^(α/β) _(i/i−1), ¹³C^(α) _(i/i−1), and¹⁵N_(i), and (c) the jointly sampling involves jointly sampling the 3chemical shift evolution periods in an indirect time domain dimension,t₁(¹³C^(α/β) _(i/i−1), ¹³C^(α) _(i/i−1), ¹⁵N_(i)).

[0126] In another alternate embodiment, the above method can bemodified, where N equals 4 and K equals 1 to conduct a (4,3)D[HNN(CO)CACBCA] GFT NMR experiment. In this method, (a) the sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (3) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) the selecting involves selecting 2 chemical shiftevolution periods of the 4D FT NMR experiment, ¹³C^(α/β) _(i−1) and¹³C^(α) _(i−1), and (c) the jointly sampling involves jointly samplingthe 2 chemical shift evolution periods in an indirect time domaindimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1)). One specific embodimentof this method ((4,3)D HNN(CO)CACBCA) involves applying radiofrequencypulses for a 4D FT NMR experiment according to the scheme shown in FIG.10.

[0127] In yet another alternate embodiment, the above method can bemodified, where N equals 4 and K equals 2 to conduct a (4,2)D[HNN(CO)CACBCA] GFT NMR experiment. In this method, (a) the sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (3) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) the selecting involves selecting 3 chemical shiftevolution periods of the 4D FT NMR experiment, ¹³C^(α/β) _(i−1), ¹³C^(α)_(i−1), and ¹⁵N_(i); and (c) the jointly sampling involves jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹⁵N_(i)).

[0128] In another alternate embodiment, the above method can bemodified, where N equals 5 and K equals 2 to conduct a (5,3)D[HNNCOCACBCA] GFT NMR experiment. In this method, (a) the sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)(α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1), (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1), (c) the jointly samplinginvolves jointly sampling the 3 chemical shift evolution periods in anindirect time domain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1)).

[0129] In yet another alternate embodiment, the above method can bemodified, where N equals 5 and K equals 3 to conduct a (5,2)D[HNNCOCACBCA] GFT NMR experiment. In this method, (a) the sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1), (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) the selecting involves selecting 4chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i); and (c) the jointlysampling involves jointly sampling the 4 chemical shift evolutionperiods in an indirect time domain dimension,

[0130] Another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 andK equals 1 to conduct a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment. Inthis method, (a) the sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i−1); (2) a polypeptide backbone amide nitrogenof amino acid residue i, ¹⁵N_(i); and (3) a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i), (b) the selecting involvesselecting 2 chemical shift evolution periods of the 4D FT NMRexperiment, ¹³C^(α/β) _(i−1) and ¹³C^(α) _(i−1), and (c) the jointlysampling involves jointly sampling the 2 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹³C^(α/β) _(i−1),¹³C^(α) _(i−1)). One specific embodiment of this method ((4,3)DCBCACA(CO)NHN) involves applying radio frequency pulses for a 4D FT NMRexperiment according to the scheme shown in FIG. 11.

[0131] In an alternate embodiment, the above method can be modified,where N equals 4 and K equals 2 to conduct a (4,2)D [CBCACA(CO)NHN] GFTNMR experiment. In this method, (a) the sample is a protein moleculehaving two consecutive amino acid residues, i−1 and i, and the chemicalshift values for the following nuclei are measured: (1) (α- andβ-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (3) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i),(b) the selecting involves selecting 3 chemical shift evolution periodsof the 4D FT NMR experiment, ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), and¹⁵N_(i), and (c) the jointly sampling involves jointly sampling the 3chemical shift evolution periods in an indirect time domain dimension,t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹⁵N_(i)).

[0132] In another alternate embodiment, the above method can bemodified, where N equals 5 and K equals 2 to conduct a (5,3)D[CBCACACONHN] GFT NMR experiment. In this method, (a) the sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)(α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1), (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1), (c) the jointly samplinginvolves jointly sampling the 3 chemical shift evolution periods in anindirect time domain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1)).

[0133] In yet another alternate embodiment, the above method can bemodified, where N equals 5 and K equals 3 to conduct a (5,2)D[CBCACACONHN] GFT NMR experiment. In this method, (a) the sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1), (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, 1 H^(N) _(i), (b) the selecting involves selecting 4chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i); (c) the jointlysampling involves jointly sampling the 4 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹³C^(α/β) _(i−1),¹³C^(α) _(i−1), ¹³C′_(i−1), ¹⁵N_(i)).

[0134] Another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 andK equals 2 to conduct a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment.In this method, (a) the sample is a protein molecule having two aminoacid residues, i and i−1, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β-protons of amino acidresidue i−1, ¹H^(α/β) _(i−1); (2) α- and β-carbons of amino acid residuei−1, ¹³C^(α/β) _(i−1); (3) a polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i); and (4) a polypeptide backbone amideproton of amino acid residue i, H^(N) _(i), (b) the selecting involvesselecting 3 chemical shift evolution periods of the 5D FT NMRexperiment, ¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), and ¹³C^(α) _(i−1), and(c) the jointly sampling involves jointly sampling the 3 chemical shiftevolution periods in an indirect time domain dimension, t₁(¹H^(α/β)_(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1)). One specific embodiment ofthis method ((5,3)D HBHACBCACA(CO)NHN) involves applying radiofrequencypulses for a 5D FT NMR experiment according to the scheme shown in FIG.12.

[0135] In an alternate embodiment, the above method can be modified,where N equals 6 and K equals 3 to conduct a (6,3)D [HBHACBCACACONHN]GFT NMR experiment. In this method, (a) the sample is a protein moleculehaving two amino acid residues, i and i−1, and the chemical shift valuesfor the following nuclei are measured: (1) α- and β protons of aminoacid residue i−1, ¹H^(α/β) _(i−1); (2) α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i−1); (3) a polypeptide backbone carbonylcarbon of amino acid residue i−1, ¹³C′_(i−1); (4) a polypeptide backboneamide nitrogen of amino acid residue i, ¹⁵N_(i); and (5) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i), (b) theselecting involves selecting 4 chemical shift evolution periods of the6D FT NMR experiment, ¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α)_(i−l, and) ¹³C′_(i−1), and (c) the jointly sampling involves jointlysampling the 4 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1)).

[0136] In another alternate embodiment, the above method can bemodified, where N equals 5 and K equals 3 to conduct a (5,2)D[HBHACBCACA(CO)NHN] GFT NMR experiment. In this method, (a) the sampleis a protein molecule having two amino acid residues, i and i−1, and thechemical shift values for the following nuclei are measured: (1) α- andβ protons of amino acid residue i−1, ¹H^(α/β) _(i−1); (2) α- andβ-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (3) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (4) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i),(b) the selecting involves selecting 4 chemical shift evolution periodsof the 5D FT NMR experiment, ¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α)_(i−1), and ¹⁵N_(i), and (c) the jointly sampling involves jointlysampling the 4 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),¹⁵N_(i)).

[0137] In yet another alternate embodiment, the above method can bemodified, where N equals 6 and K equals 4 to conduct a (6,2)D[HBHACBCACACONHN] GFT NMR experiment. In this method, (a) the sample isa protein molecule having two amino acid residues, i and i−1, and thechemical shift values for the following nuclei are measured: (1) α- andβ protons of amino acid residue i−1, ¹H^(α/β) _(i−1); (2) α- andβ-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (3) a polypeptidebackbone carbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (5) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) the selecting involves selecting 5 chemical shiftevolution periods of the 6D FT NMR experiment, ¹H^(α/β) _(i−1),¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i), and (c) thejointly sampling involves jointly sampling the 5 chemical shiftevolution periods in an indirect time domain dimension, t₁(¹H^(α/β)_(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), ¹⁵N_(i)).

[0138] Yet another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 andK equals 2 to conduct a (5,3)D [HCC,CH—COSY] GFT NMR experiment. In thismethod, (a) the chemical shift values for the following nuclei aremeasured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; and (3) acarbon coupled to ¹³C, ¹³C^(coupled); and (4) a proton coupled to¹³C^(coupled), ¹H^(coupled), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹H, ¹³C,and ¹³C^(coupled), and (c) the jointly sampling involves jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H, ¹³C, ¹³C^(coupled)). The sample in this methodcan be any molecule such as (metallo)-organic molecules and complexes,nucleic acid molecules such as DNA and RNA, lipids, or polymers. In oneembodiment, the chemical shift evolution periods for ¹³C and¹³C^(coupled) can be correlated using total correlation spectroscopy(TOCSY) (Ernst et al., Principles of Nuclear Magnetic Resonance in Oneand Two Dimensions, Clarendon, Oxford (1987), which is herebyincorporated by reference in its entirety). In another embodiment, (a)the sample is a protein molecule having an amino acid residue, i, andthe chemical shift values for the following nuclei are measured: (1) aproton of amino acid residue i, ¹H_(i); (2) a carbon of amino acidresidue i coupled to ¹H_(i), ¹³C_(i); and (3) a carbon coupled to¹³C_(i), ¹³C_(i) ^(coupled); and (4) a proton coupled with ¹³C_(i)^(coupled), ¹H_(i) ^(coupled), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹H_(i),¹³C_(i), and ¹³C_(i) ^(coupled), and (c) the jointly sampling involvesjointly sampling the 3 chemical shift evolution periods in an indirecttime domain dimension, t₁(¹H_(i), ¹³C_(i), ¹³C_(i) ^(coupled)). Onespecific embodiment of this method ((5,3)D HCC,CH—COSY) involvesapplying radiofrequency pulses for a 5D FT NMR experiment according tothe scheme shown in FIG. 13.

[0139] The present invention also relates to the above method ofconducting a (N,N−K)D GFT NMR experiment, where N equals 5 and K equals2 to conduct a (5,3)D [HBCBCGCDHD] GFT NMR experiment. In this method,(a) the sample is a protein molecule having an amino acid residue, i,with an aromatic side chain, and the chemical shift values for thefollowing nuclei are measured: (1) a β-proton of amino acid residue i,¹H^(β) _(i); (2) a β-carbon of amino acid residue i, ¹³C^(β) _(i); (3) aγ-carbon of amino acid residue i, ¹³C^(γ) _(i); (4) a δ-carbon of aminoacid residue i, ¹³C^(δ) _(i); and (5) a δ-proton of amino acid residuei, ¹H^(N) _(i), (b) the selecting involves selecting 3 chemical shiftevolution periods of the 5D FT NMR experiment, ¹H^(β) _(i), ¹³C^(β)_(i), and ¹³C^(δ) _(i), and (c) the jointly sampling involves jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(N) _(i), ¹³C^(β) _(i), ¹³C^(δ) _(i)). Onespecific embodiment of this method ((5,3)D HBCBCGCDHD) involves applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG. 14.

[0140] In an alternate embodiment, the above method can be modified,where N equals 5 and K equals 3 to conduct a (5,2)D [HBCBCGCDHD] GFT NMRexperiment. In this method, (a) the sample is a protein molecule havingan amino acid residue, i, with an aromatic side chain, and the chemicalshift values for the following nuclei are measured: (1) a β-proton ofamino acid residue i, ¹H^(β) _(i); (2) a β-carbon of amino acid residuei, ¹³C^(β) _(i); (3) a γ-carbon of amino acid residue i; (4) a δ-carbonof amino acid residue i, ¹³C^(δ) _(i); and (5) a δ-proton of amino acidresidue i, ¹H^(δ) _(i), (b) the selecting involves selecting 4 chemicalshift evolution periods of the 5D FT NMR experiment, ¹H^(β) _(i),¹³C^(β) _(i), ¹³C^(γ) _(i), and ¹³C^(δ) _(i), and (c) the jointlysampling involves jointly sampling the 4 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H^(β) _(i), ¹³C^(β)_(i), ¹³C^(γ) _(i), ¹³C^(δ) _(i)).

[0141] Another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 4 andK equals 2 to conduct a (4,2)D [HCCH—COSY] GFT NMR experiment. In thismethod, (a) the chemical shift values for the following nuclei aremeasured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) acarbon coupled to ¹³C, ¹³C^(coupled); and (4) a proton coupled to¹³C^(coupled), ¹H^(coupled), (b) the selecting involves selecting 3chemical shift evolution periods of the 4D FT NMR experiment, ¹H, ¹³C,and ¹³C^(coupled), and (c) the jointly sampling involves jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H, ¹³C, ¹³C^(coupled)). The sample in this methodcan be any molecule such as (metallo)-organic molecules and complexes,nucleic acid molecules such as DNA and RNA, lipids, or polymers. In oneembodiment, the chemical shift evolution periods for ¹³C and¹³C^(coupled) are correlated using total correlation spectroscopy(TOCSY). In another embodiment, (a) the sample is a protein moleculehaving an amino acid residue, i, and the chemical shift values for thefollowing nuclei are measured: (1) a proton of amino acid residue i,¹H_(i); (2) a carbon of amino acid residue i coupled to ¹H_(i), ¹³C_(i);(3) a carbon coupled to ¹³C_(i), ¹³C_(i) ^(coupled); and (4) a protoncoupled to ¹³C_(i) ^(coupled), ¹H_(i) ^(coupled), (b) the selectinginvolves selecting 3 chemical shift evolution periods of the 4D FT NMRexperiment, ¹H_(i), ¹³C_(i), and ¹³C_(i) ^(coupled), and (c) the jointlysampling involves jointly sampling the 3 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H_(i), ¹³C_(i),¹³C_(i) ^(coupled)). One specific embodiment of this method ((4,2)DHCCH—COSY) involves applying radiofrequency pulses for a 4D FT NMRexperiment according to the scheme shown in FIG. 15.

[0142] Yet another aspect of the present invention relates to the abovemethod of conducting a (N,N−K)D GFT NMR experiment, where N equals 5 andK equals 3 to conduct a (5,2)D [HCCCH—COSY] GFT NMR experiment. In thismethod, (a) the chemical shift values for the following nuclei aremeasured: (1) a proton ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) a carboncoupled to ¹³C, ¹³C^(coupled); (4) a carbon coupled to ¹³C^(coupled),¹³C^(coupled-2); and (5) a proton coupled with ¹³C^(coupled-2),¹H^(coupled-2), (b) the selecting involves selecting 4 chemical shiftevolution periods of the 5D FT NMR experiment, H, ¹³C, ¹³C^(coupled),and ¹³C^(coupled-2) and (c) the jointly sampling involves jointlysampling the 4 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H, ¹³C, ¹³C^(coupled), ¹³C^(coupled-2)). Thesample in this method can be any molecule such as (metallo)-organicmolecules and complexes, nucleic acid molecules such as DNA and RNA,lipids, or polymers. In one embodiment, (a) the sample is a proteinmolecule having an amino acid residue, i, and the chemical shift valuesfor the following nuclei are measured: (1) a proton of amino acidresidue i, ¹H_(i); (2) a carbon of amino acid residue i coupled to¹H_(i), ¹³C_(i); (3) a carbon coupled to ¹³C_(i), ¹³C_(i) ^(coupled);(4) a carbon coupled to ¹³C_(i) ^(coupled), ¹³C_(i) ^(coupled) ²; and(5) a proton coupled with ¹³C_(i) ^(coupled-2), ¹H_(i) ^(coupled-2), (b)the selecting involves selecting 4 chemical shift evolution periods ofthe 5D FT NMR experiment, ¹H_(i), ¹³C_(i), ¹³C_(i) ^(coupled) and¹³C_(i) ^(coupled-2), and (c) the jointly sampling involves jointlysampling the 4 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H_(i), ^(—C) _(i), ¹³C_(i) ^(coupled), ¹³C_(i)^(coupled-2)).

[0143] In an alternate embodiment, the above method can be modified,where N equals 5 and K equals 3 to conduct a (5,3)D [HCCCH—COSY] GFT NMRexperiment. In this method, (a) the chemical shift values for thefollowing nuclei are measured: (1) a proton, ¹H; (2) a carbon coupled to¹H, ¹³C; (3) a carbon coupled to ¹³C, ¹³C^(coupled); (4) a carboncoupled to ¹³C^(coupled), ¹³C^(coupled-2); and (5)a proton coupled with¹³C^(coupled-2), ¹H^(coupled-2), (b) the selecting involves selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹H, ¹³C,and ¹³C^(coupled), and (c) the jointly sampling involves jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H, ¹³C, ¹³C^(coupled)). The sample in this methodcan be any molecule such as (metallo)-organic molecules and complexes,nucleic acid molecules such as DNA and RNA, lipids, or polymers. Inanother embodiment, (a) the sample is a protein molecule having an aminoacid residue, i, and the chemical shift values for the following nucleiare measured: (1) a proton of amino acid residue i, ¹H_(i); (2) a carbonof amino acid residue i coupled to ¹H_(i), ¹³C_(i); (3) a carbon coupledto ¹³C_(i), ¹³C_(i) ^(coupled); (4) a carbon coupled to ¹³C_(i)^(coupled), ¹³C_(i) ^(coupled-2); and (5) a proton coupled with ¹³C_(i)^(coupled-2), ¹H_(i) ^(coupled-2), (b) the selecting involves selecting3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H_(i),¹³C_(i), and ¹³C_(i) ^(coupled) (c) the jointly sampling involvesjointly sampling the 3 chemical shift evolution periods in an indirecttime domain dimension, t₁(¹H_(i), ¹³C_(i) ^(coupled)).

[0144] Combinations of GFT NMR Experiments

[0145] A set of multidimensional GFT NMR experiments enables one todevise strategies for GFT NMR-based (high throughput) resonanceassignment of proteins or other molecules.

[0146] Thus, another aspect of the present invention relates to a methodfor sequentially assigning chemical shift values of an α-proton, ¹H^(α)an α-carbon, ¹³C^(α), a polypeptide backbone carbonyl carbon, ¹³C′, apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H, of a protein molecule. The method involves providing aprotein sample and conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (5,2)D [HACACONHN] GFT NMR experiment to measure andconnect the chemical shift values of the α-proton of amino acid residuei−1, ¹H^(α) _(i−1), the α-carbon of amino acid residue i−1, ¹³C^(α)_(i−1), the polypeptide backbone carbonyl carbon of amino acid residuei−1, ¹³C′_(i−1), the polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i), and the polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i) and (2) a (5,2)D [HACA,CONHN] GFT NMRexperiment to measure and connect the chemical shift values of ¹H^(α)_(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), the polypeptide backbone amidenitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, ¹H^(N) _(i−1). Then,sequential assignments of the chemical shift values of ¹H^(α), ¹³C^(α),¹³C′, ¹⁵N, and ¹H^(N) are obtained by (i) matching the chemical shiftvalues of ¹H^(α) _(i−1,) ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the(5,2)D [HACACONHN] GFT NMR experiment with the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the (5,2)D[HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) to identify the type ofamino acid residue i−1 (Wüthrich, NMR of Proteins and Nucleic Acids,Wiley, N.Y. (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993),which are hereby incorporated by reference in their entirety), and (iii)mapping sets of sequentially connected chemical shift values to theamino acid sequence of the polypeptide chain and using the chemicalshift values to locate secondary structure elements (such as α-helicesand β-sheets) within the polypeptide chain (Spera et al., J. Am. Chem.Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651(1992), which are hereby incorporated by reference in their entirety).

[0147] Yet another aspect of the present invention relates to a methodfor sequentially assigning chemical shift values of an α-proton, ¹H^(α),an α-carbon, ¹³C^(α), a polypeptide backbone carbonyl carbon, ¹³C′, apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H^(N), of a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (5,3)D [HACACONHN] GFT NMR experiment tomeasure and connect the chemical shift values of the α-proton of aminoacid residue i−1, ¹H^(α) _(i−1), the α-carbon of amino acid residue i−1,¹³C^(α) _(i−1), the polypeptide backbone carbonyl carbon of amino acidresidue i−1, ¹³C′_(i−1), the polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i), and the polypeptide backbone amide protonof amino acid residue i, ¹H^(N) _(i) and (2) a (5,3)D [HACA,CONHN]0 GFTNMR experiment to measure and connect the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), the polypeptide backboneamide nitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, ¹H^(N) _(i−1). Then,sequential assignments of the chemical shift values of ¹H^(α), ¹³C^(α,)¹³C′, ¹⁵N, and ¹H^(N) are obtained by (i) matching the chemical shiftvalues of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the(5,3)D [HACACONHN] GFT NMR experiment with the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by the (5,3)D[HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) to identify the type ofamino acid residue i−1 (Wüthrich, NMR of Proteins and Nucleic Acids,Wiley, N.Y. (1986); Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993),which are hereby incorporated by reference in their entirety), and (iii)mapping sets of sequentially connected chemical shift values to theamino acid sequence of the polypeptide chain and using the chemicalshift values to locate secondary structure elements (such as α-helicesand β-sheets) within the polypeptide chain (Spera et al., J. Am. Chem.Soc., 113:5490-5492 (1991); Wishart et al., Biochemistry, 31:1647-1651(1992), which are hereby incorporated by reference in their entirety).

[0148] A further aspect of the present invention relates to a method forsequentially assigning chemical shift values of α- and β-carbons,¹³C^(α/β), a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptidebackbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton,¹H^(N), of a protein molecule. The method involves providing a proteinsample and conducting a set of G matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (4,3)D [CBCACONHN] GFT NMR experiment to measure andconnect the chemical shift values of the α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i−1), the polypeptide backbone carbonyl carbonof amino acid residue i−1, ¹³C′_(i−1), the polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i), and the polypeptide backboneamide proton of amino acid residue i, ¹H^(N) _(i) and (2) a (4,3)D[CBCA,CONHN] GFT NMR experiment to measure and connect the chemicalshift values of ¹³C^(α/β) _(i−1), ¹³C′_(i−1), the polypeptide backboneamide nitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, H^(N) _(i−1). Then,sequential assignments of the chemical shift values of ¹³C^(α/β), ¹³C′,¹⁵N, and ¹H^(N) are obtained by (i) matching the chemical shift valuesof ¹³C^(α/β) _(i−1) and ¹³C′_(i−1) measured by the (4,3)D [CBCACONHN]GFT NMR experiment with the chemical shift values of ¹³C^(α/β) _(i−1)and ¹³C′_(i−1) measured by the (4,3)D [CBCA, CONHN] GFT NMR experiment,(ii) using the chemical shift values of ¹³C^(α/β) _(i−1) and ¹³C′_(i−1)to identify the type of amino acid residue i−1 (Wüthrich, NMR ofProteins and Nucleic Acids. Wiley, N.Y. (1986); Grzesiek et al., J.Biomol. NMR. 3: 185-204 (1993), which are hereby incorporated byreference in their entirety), and (iii) mapping sets of sequentiallyconnected chemical shift values to the amino acid sequence of thepolypeptide chain and using the chemical shift values to locatesecondary structure elements (such as α-helices and β-sheets) within thepolypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492(1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which arehereby incorporated by reference in their entirety).

[0149] The present invention also relates to a method for sequentiallyassigning chemical shift values of α- and β-carbons, ¹³C^(α/β), apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H^(N), of a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment tomeasure and connect the chemical shift values of the α- and β-carbons ofamino acid residue i−1, ¹³C^(α/β) _(i−1), the α-carbon of amino acidresidue i−1, ¹³C^(α) _(i−1), the polypeptide backbone amide nitrogen ofamino acid residue i−1, ¹⁵N_(i−1), and the polypeptide backbone amideproton of amino acid residue i−1, ¹H^(N) _(i−1) and (2) a GFT NMRexperiment selected from the group consisting of a (4,3)D[HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMRexperiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment tomeasure and connect the chemical shift values of ¹³C^(α/β) _(i−1),¹³C^(α) _(i−1), the polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i), and the polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i). Then, sequential assignments of thechemical shift values of ¹³C^(α/β), ¹⁵N, and ¹H^(N) are obtained by (i)matching the chemical shift values of ¹³C^(α/β) _(i−1) measured by theGFT NMR experiment selected from the group consisting of a (4,3)D[HNN(CO)CACBCA] GFT NMR experiment, a (4,3)D [CBCACA(CO)NHN] GFT NMRexperiment, and a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment with thechemical shift values of ¹³C^(α/β) _(i−1) measured by the (4,3)D[HNNCACBCA] GFT NMR experiment, (ii) using the chemical shift values of¹³C^(α/β) _(i−1) to identify the type of amino acid residue i−1(Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, N.Y. (1986);Grzesiek et al., J. Biomol. NMR, 3: 185-204 (1993), which are herebyincorporated by reference in their entirety), and (iii) mapping sets ofsequentially connected chemical shift values to the amino acid sequenceof the polypeptide chain and using the chemical shift values to locatesecondary structure elements (such as α-helices and β-sheets) within thepolypeptide chain (Spera et al., J. Am. Chem. Soc., 113:5490-5492(1991); Wishart et al., Biochemistry, 31:1647-1651 (1992), which arehereby incorporated by reference in their entirety).

[0150] Another aspect of the present invention relates to a method forassigning chemical shift values of γ-, δ-, and ε-aliphatic sidechainprotons, ¹H^(γ/δ/ε), and chemical shift values of γ-, δ-, andε-aliphatic sidechain carbons located peripheral to β-carbons,¹³C^(γ/δ/ε), of a protein molecule. The method involves providing aprotein sample and conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (5,3)D [HCC,CH—COSY] GFT NMR experiment to measure andconnect the chemical shift values of a proton of amino acid residue i−1,¹H_(i−1), a carbon of amino acid residue i−1 coupled to ¹H_(i−1),¹³C_(i−1), a carbon coupled to ¹³C_(i−1), ¹³C^(α) _(i−1) ^(coupled), anda proton coupled to ¹³C−1 ^(coupled), ¹H^(N) _(i−1) ^(coupled), and (2)a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connectthe chemical shift values of α- and β-protons of amino acid residue i−1,¹H^(α/β) _(i−1), and α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1). Then, assignments of the chemical shift values of¹H^(γ/δ/ε) and ¹³C^(γ/δ/ε) are obtained by (i) identifying ¹H_(i−1),¹³C_(i−1), ¹³C_(i−1) ^(coupled), and ¹H_(i−1) ^(coupled) measured by the(5,3)D [HCC,CH—COSY] GFT NMR experiment as ¹H^(α) _(i−1), ¹³C^(α)_(i−1), ¹³C^(β) _(i−1), and ¹H^(β) _(i−1), respectively, and therebymatching the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) with the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and(ii) using the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) in conjunction with other chemical shift connections from the(5,3)D [HCC,CH—COSY] GFT NMR experiment to measure the chemical shiftvalues of ¹H^(γ/δ/ε) _(i−1) and ¹³C^(γ/δ/ε) _(i−1).

[0151] Yet another aspect of the present invention relates to a methodfor assigning chemical shift values of γ-, δ-, and ε-aliphatic sidechainprotons, ¹H^(γ/δ/ε), and chemical shift values of γ-, δ-, andε-aliphatic sidechain carbons located peripheral to β-carbons,¹³C^(γ/δ/ε), of a protein molecule. The method involves providing aprotein sample and conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein sampleincluding: (1) a (4,2)D [HCCH—COSY] GFT NMR experiment to measure andconnect the chemical shift values of a proton of amino acid residue i−1,¹H_(i−1), a carbon of amino acid residue i−1 coupled to ¹H_(i−1),¹³C_(i−1), a carbon coupled to ¹³C_(i−1), ¹³C _(i−1) ^(coupled), and aproton coupled to ¹³C_(i−1) ^(coupled), ¹H_(i−1) ^(coupled), and (2) a(5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect thechemical shift values of α- and β-protons of amino acid residue i−1,¹H^(α/β) _(i−1), and α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1). Then, assignments of the chemical shift values of¹H^(γ/δ/ε) and ¹³C^(γ/δ/ε) are obtained by (i) identifying ¹H_(i−1),¹³C_(i−1), ¹³ ^(C) _(i−1) ^(coupled), and ¹H^(N) _(i−1) ^(coupled)measured by the (4,2)D [HCCH—COSY] GFT NMR experiment as ¹H^(α) _(i−1),¹³C^(α) _(i−1), ¹³Cβ_(i−1), and ¹H^(β) _(i−1), respectively, and therebymatching the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) with the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β)_(i−1) measured by the (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and(ii) using the chemical shift values of ¹H^(α/β) _(i−1), and ¹³C^(α/β)_(i−1) in conjunction with other chemical shift connections from the(4,2)D [HCCH—COSY] GFT NMR experiment to measure the chemical shiftvalues of ¹H^(γ/δ/ε) _(i−1) and ¹³C^(γ/δ/ε) _(i−1).

[0152] A further aspect of the present invention relates to a method forassigning chemical shift values of a γ-carbon, ¹³C^(γ), a δ-carbon,¹³C^(δ), and a δ-proton, ¹H5, of an amino acid residue containing anaromatic spin system in a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a (5,3)D [HBCBCGCDHD] GFT NMR experimentto measure and connect the chemical shift values of a β-proton of aminoacid residue i−1, ¹H^(β) _(i−1), a β-carbon of amino acid residue i−1,¹³C^(β) _(i−1), a δ-carbon of amino acid residue i−1, ¹³C^(γ) _(i−1), aδ-carbon of amino acid residue i−1, ¹³C^(δ) _(i−1), and a δ-proton ofamino acid residue i−1, ¹H^(δ) _(i−1), and (2) a (5,3)D[HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect thechemical shift values of ¹H^(β) _(i−1) and ¹³C^(β) _(i−1). Then,assignments of the chemical shift values of ¹³C^(γ), ¹³C^(δ), and ¹H^(δ)are obtained by (i) matching the chemical shift values of ¹H^(β) _(i−1)and ¹³C^(β) _(i−1) measured by the (5,3)D HBCBCACA(CO)NHN GFT NMRexperiment with the chemical shift values of ¹H^(β) _(i−1) and ¹³C^(β)_(i−1) measured by the (5,3)D [HBCBCGCDHD] GFT NMR experiment, and (ii)using the chemical shift values of ¹³C^(γ), ¹³C^(δ), and ¹H^(δ) toidentify the type of amino acid residue containing the aromatic spinsystem.

[0153] The present invention also relates to a method for assigningchemical shift values of aliphatic and aromatic protons and aliphaticand aromatic carbons of an amino acid residue containing aliphatic andaromatic spin systems in a protein molecule. The method involvesproviding a protein sample and conducting a set of G matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments on theprotein sample including: (1) a first GFT NMR experiment, which isselected from the group consisting of a (5,3)D [HCC,CH—COSY] GFT NMRexperiment, a (4,2)D [HCCH—COSY] GFT NMR experiment, a (5,2)D[HCCCH—COSY] GFT NMR experiment, and a (5,3)D [HCCCH—COSY] GFT NMRexperiment and is acquired for the aliphatic spin system, to measure andconnect the chemical shift values of α- and β-protons of amino acidresidue i, ¹H^(α/β) _(i), α- and β-carbons of amino acid residue i,¹³C^(α/β) _(i), a γ-carbon of amino acid residue i, ¹³C^(γ) _(i), and(2) a second GFT NMR experiment, which is selected from the groupconsisting of a (5,3)D [HCC,CH—COSY] GFT NMR experiment, a (4,2)D[HCCH—COSY] GFT NMR experiment, a (5,2)D [HCCCH—COSY] GFT NMRexperiment, and a (5,3)D [HCCCH—COSY] GFT NMR experiment and is acquiredfor the aromatic spin system, to measure and connect the chemical shiftvalues of ¹³C^(γ) _(i) and other aromatic protons and carbons of aminoacid residue i. Then, assignments of the chemical shift values of thealiphatic and aromatic protons and aliphatic and aromatic carbons areobtained by matching the chemical shift value of ¹³C^(γ) _(i) measuredby the first GFT NMR experiment with the chemical shift value of ¹³C^(γ)_(i) measured by the second GFT NMR experiment. In another embodiment,the set of GFT NMR experiments can be conducted by using ¹³C^(γ)steadystate magnetization to generate first order central peaks.

[0154] The above-described methods for assigning chemical shift valuesin a protein molecule can involve further subjecting the protein sampleto nuclear Overhauser enhancement spectroscopy (NOESY) (Wüthrich, NMR ofProteins and Nucleic Acids, Wiley, N.Y. (1986), which is herebyincorporated by reference in its entirety), to NMR experiments thatmeasure scalar coupling constants (Eberstadt et al., Angew. Chem. Int.Ed. Engl., 34:1671-1695 (1995); Cordier et al., J. Am. Chem. Soc.,121:1601-1602 (1999), which are hereby incorporated by reference intheir entirety), or to NMR experiments that measure residual dipolarcoupling constants (Prestegard, Nature Struct. Biol., 5:517-522 (1998);Tjandra et al., Science, 278:1111-1114 (1997), which are herebyincorporated by reference in their entirety), to deduce the tertiaryfold or tertiary structure of the protein molecule.

[0155] Another aspect of the present invention relates to a method forobtaining assignments of chemical shift values of ¹H, ¹³C, and ¹⁵N of aprotein molecule. The method involves providing a protein sample andconducting five G matrix Fourier transformation (GFT) nuclear magneticresonance (NMR) experiments on the protein sample, where (1) a firstexperiment is a (4,3)D [HNNCACBCA] GFT NMR experiment for obtainingintraresidue correlations of chemical shift values; (2) a secondexperiment is a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment forobtaining interresidue correlations of chemical shift values; (3) athird experiment is a (5,3)D [HCC,CH—COSY] GFT NMR experiment forobtaining assignments of aliphatic sidechain chemical shift values; (4)a fourth experiment is a (5,3)D [HBCBCGCDHD] GFT NMR experiment forlinking chemical shift values of aliphatic protons, ¹H^(β) and ¹³C^(β),and aromatic protons, ¹³C^(δ) and ¹H^(δ); and (5) a fifth experiment isa (4,2)D [HCCH—COSY] GFT NMR experiment for obtaining assignments ofaromatic sidechain chemical shift values. These five GFT NMR experimentscan be employed for obtaining nearly complete resonance assignments ofproteins including aliphatic and aromatic side chain spin systems.

EXAMPLES

[0156] The following examples are provided to illustrate embodiments ofthe present invention but are by no means intended to limit its scope.

Example 1 Frequency Domain Editing of Chemical Shift Multiplets andRelation to the Formalism for Time Domain Editing

[0157] When designing a GFT NMR experiment (FIG. 1), one firstidentifies a “target” dimensionality, N_(t), at which the majority ofthe peaks are resolved. The dimensionality N of a given FT NMR spectrumis then adapted to N_(t) by jointly sampling K+1 chemical shifts(K=N−N_(t)) in a hypercomplex manner, while N_(t)−1 dimensions aresampled in a conventional fashion. As outlined, this yields 2^(K) N_(t)Dspectra. As an example, the case of K=3 in the frequency domain (FIGS.2, 16, and 17) is described in this example. The indirect evolution timeshall be t, and Ω₀ shall be the chemical shift detected in quadrature ineach of the N_(t)D spectra. Ω₁, Ω₂ and Ω₃ are the three jointly sampledshifts. The phases of the 90° pulses generating transverse magnetizationfor frequency labeling are chosen so that the transfer amplitudes of thereal parts of the 2^(K)=8 spectra, Sjr (=1 . . . 8) are proportional to:

[0158] S1r∝ cos(Ω₀t) cos(Ω₁t) cos(Ω₂t) cos(Ω₃t)

[0159] S2r∝ cos(Ω₀t) sin(Ω₁t) cos(Ω₂t) cos(Ω₃t)

[0160] S3r∝ cos(Ω₀t) cos(Ω₁t) sin(Ω₂t) cos(Ω₃t)

[0161] S4r∝ cos(Ω₀t) sin(Ω₁t) sin(Ω₂t) cos(Ω₃t)

[0162] S5r∝ cos(Ω₀t) cos(Ω₁t) cos(Ω₂t) sin(Ω₃t)

[0163] S6r∝ cos(Ω₀t) sin(Ω₁t) cos(Ω₂t) sin(Ω₃t)

[0164] S7r∝ cos(Ω₀t) cos(Ω₁t) sin(Ω₂t) sin(Ω₃t)

[0165] S8r∝ cos(Ω₀t) sin(Ω₁t) sin(Ω₂t) sin(Ω₃t).

[0166] FT and, depending on the number n of chemical shift sinemodulations the application of a zero-order phase correction of n·90°yields the frequency domain spectra A1 . . . A8. These spectra encodeΩ₁, Ω₂, and Ω₃ in signal splittings of “chemical shift multiplets” eachcomprising 2^(K)=8 components. Cosine and sine modulations give rise(Ernst et al., Principles of Nuclear Magnetic Resonance in One and TwoDimensions, Clarendon, Oxford (1987), which is hereby incorporated byreference in its entirety) to in-phase and anti-phase splittings,respectively, and linear combinations of spectra A1 . . . A8 providespectra B1 . . . B8 with peaks only at the frequencies of the individualmultiplet components. Spectrum B1: Ω₀+Ω₁+Ω₂+Ω₃, B2: Ω₀−Ω₁+Ω₂+Ω₃, B3:Ω₀+Ω₁−Ω₂+Ω₃, B4: Ω₀−Ω₁−Ω₂+Ω₃, B5: Ω₀+Ω₁+Ω₂−Ω₃, B6: Ω₀−Ω₁+Ω₂−Ω₃, B7:Ω₀+Ω₁−Ω₂−Ω₃, and B8: Ω₀−Ω₁−Ω₂−Ω₃ (FIG. 2). Spectra B1 to B8 are the“basic spectra”, and the selection of chemical shift multipletcomponents represents the phase-sensitive “editing of chemical shiftmultiplets”.

[0167] Acquisition of peaks defining the centers of the chemical shiftsplittings (“central peaks”) is required for unambiguous assignment, iftwo chemical shift quartets, (Ω₀, Ω₁, Ω₂, Ω₃) and (Ω′₀, Ω′₁, Ω′₂, Ω′₃),are correlated with degenerate chemical shifts in the other N_(t)−1dimensions. Furthermore, degeneracy may occur between two or more shiftsof the quartet itself, e.g., one may have that Ω₁=Ω_(′) ₁. Theinformation of the ND experiment resolving degeneracy in up to N−1dimensions, is made available if central peaks are detected. First,spectra with transfer amplitudes of the real parts of 2^(K−1)=4 spectra,Sjr (j=9 . . . 12), encode Ω₁ and Ω₂, but no Ω₃ signal splittings,

S9r∝ cos(Ω₀ t) cos(Ω₁ t) cos(Ω₂ t)

S10r∝ cos(Ω₀ t) sin(Ω₁ t) cos(Ω₂ t)

S11r∝ cos(Ω₀ t) cos(Ω₁ t) sin(Ω₂ t)

S12r∝ cos(Ω₀ t) sin(Ω₁ t) sin(Ω₂ t)

[0168] and provide the centers of the Ω₃-splittings. S9 . . . S12 yield,as described, spectra B9 . . . B12 with peaks at: B9: Ω₀+Ω₁+Ω₂, B10:Ω₀−Ω₂+Ω₂, B11: Ω₀+Ω₁−Ω₂, B12: Ω₀−Ω₂. Second, spectra with transferamplitudes for the real parts 2^(K−2)=2 spectra, Sjr (1=13, 14), encodeonly Ω₁-signal splittings

S13r∝ cos(Ω₀ t) cos(Ω₁ t)

S14r∝ cos(Ω₀ t) sin(Ω₂ t)

[0169] and provide the centers of the Ω₂-splittings. S13 and S14 yieldB13 and B14 comprising peaks at: B13: Ω₀+Ω₁, B14: Ω₀−Ω₁. Third,2^(K−3)=1 spectrum, S15 with a transfer amplitude for the real partencoding no signal splittings,

S15r∝ cos(Ω₀ t)

[0170] provides the centers of the Ω₁-splittings.

[0171] GFT NMR data acquisition (FIG. 1) requires recording of a totalof $p = {{\sum\limits_{k = 0}^{K}2^{k}} = {2^{K + 1} - 1}}$

[0172] N_(t)D spectra (e.g., S1 . . . S15 for K=3) with 2^(K) basicspectra and a total of 2^(K−1) central peak spectra. This set of p datasets is designated an “(N,N_(t))D GFT NMR experiment”, and central peaksdue to omission of m chemical shifts are denoted to be of m-th order(e.g., B9 . . . B12, B13, B14, and B15 represent first, second and thirdorder central peaks, respectively).

[0173] For frequency domain editing, the data sets S1 . . . S15 areFourier transformed to yield spectra A1 . . . A15 (FIG. 2), and,depending on the number n of chemical shift sine modulations, azero-order phase correction of n·90° is applied. Subsequent linearcombination yields the edited spectra B1 . . . B15 (FIGS. 16 and 17)according to

{circumflex over (B)}(K)={circumflex over (F)}(K)·Â(K)  (4),

[0174] where {circumflex over (F)}(K) can be readily obtained from{circumflex over (F)}(K−1) by tensor product formation:

{circumflex over (F)}(K)={circumflex over (F)}(K−1)⊕{circumflex over(F)}(1)  with

[0175] $\begin{matrix}{{\overset{\Cap}{F}(1)} = {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}.}} & (5)\end{matrix}$

[0176] One thus obtains for K=2 $\begin{matrix}{{\begin{bmatrix}{B9} \\{B10} \\{B11} \\{B12}\end{bmatrix} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix} \cdot \begin{bmatrix}{A9} \\{A10} \\{A11} \\{A12}\end{bmatrix}}},{{{and}\quad {for}\quad K} = 3}} & (6) \\{\begin{bmatrix}{B1} \\{B2} \\{B3} \\{B4} \\{B5} \\{B6} \\{B7} \\{B8}\end{bmatrix} = {\begin{bmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} & 1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1 & 1 & {- 1} & {- 1} & 1 \\1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} & {- 1} & 1 & {- 1} & 1 \\1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\1 & {- 1} & {- 1} & 1 & {- 1} & 1 & 1 & {- 1}\end{bmatrix} \cdot {\begin{bmatrix}{A1} \\{A2} \\{A3} \\{A4} \\{A5} \\{A6} \\{A7} \\{A8}\end{bmatrix}.}}} & (7)\end{matrix}$

[0177] The equations for K=1 $\begin{matrix}{{\begin{bmatrix}{B13} \\{B14}\end{bmatrix} = {\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix} \cdot \begin{bmatrix}{A13} \\{A14}\end{bmatrix}}},} & (8)\end{matrix}$

 and for K=0

B15=A15  (9),

[0178] are likewise given here.

[0179] The matrices Ĝ(K) and {circumflex over (F)}(K) for time andfrequency domain editing of chemical shift multiplets (FIGS. 1 and 2)are related to each other according to Ĝ(K)=Ĥ(K) ·{circumflex over(P)}(K) with${\overset{\Cap}{H}(K)} = {{{\overset{\Cap}{F}(K)} \otimes \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}} \cdot {\overset{\Cap}{H}(K)}}$

[0180] applies the addition scheme of {circumflex over (F)}(K) (equation5) to both real and imaginary parts. To derive {circumflex over (P)}(K),${{\overset{\Cap}{P}}^{\prime}(1)} = \begin{bmatrix}\overset{\Cap}{E} & 0 \\0 & \hat{P}\end{bmatrix}$

[0181] is first defined with $\overset{\Cap}{E} = {{\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}\quad {and}\quad \hat{P}} = {\begin{bmatrix}0 & {- 1} \\1 & 0\end{bmatrix}.}}$

[0182] The matrix {circumflex over (P)} maps the real onto theimaginary, and the imaginary onto the negative real part. Thiscorresponds to a zero-order 90° phase correction in the frequencydomain. Accordingly, application of {circumflex over (P)}^(n)corresponds to applying the n·90° zero-order phase correction alluded toabove. {circumflex over (P)}′(K+1) can be constructed from the{circumflex over (P)}′(K) according to${{\overset{\Cap}{P}}^{\prime}\left( {K + 1} \right)} = {{{\overset{\Cap}{P}}^{\prime}(K)} \otimes {\begin{bmatrix}\overset{\Cap}{E} & 0 \\0 & \overset{\Cap}{P}\end{bmatrix}.}}$

[0183] Expansion of the products of Ê and {circumflex over (P)}resulting “after” (multiple) tensor product formation yields {circumflexover (P)}(K), a matrix with a 2×2 block diagonal form.

[0184] For K=3, 2, and 1, thus, the following is obtained for Ĥ(K) and{circumflex over (P)}(K). ${{\overset{\Cap}{H}(3)} = \begin{bmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 \\0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} \\1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 \\0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 \\1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} \\1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 \\0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 \\1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 & 1 & 0 & 1 & 0 & {- 1}\end{bmatrix}},{{\overset{\Cap}{H}(2)} = \begin{bmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1} & 0 & 1 & 0 & {- 1} \\1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 \\0 & 1 & 0 & 1 & 0 & {- 1} & 0 & {- 1} \\1 & 0 & {- 1} & 0 & {- 1} & 0 & 1 & 0 \\0 & 1 & 0 & {- 1} & 0 & {- 1} & 0 & 1\end{bmatrix}},{{\overset{\Cap}{H}(1)} = {{\begin{bmatrix}1 & 0 & 1 & 0 \\0 & 1 & 0 & 1 \\1 & 0 & {- 1} & 0 \\0 & 1 & 0 & {- 1}\end{bmatrix}\quad {and}\quad {\overset{\Cap}{P}(3)}} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0\end{bmatrix}}},{{\overset{\Cap}{P}(2)} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1}\end{bmatrix}},{{\overset{\Cap}{P}(1)} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & {- 1} \\0 & 0 & 1 & 0\end{bmatrix}.}}$

Example 2 Options to Implement Central Peak Acquisition in GFT NMR

[0185] The successive identification of peak pairs belonging to centralpeaks of decreasing order ensures the unambiguous assignment of chemicalshift multiplet components (FIGS. 2 and 3). Such central peakacquisition can be achieved in three different ways. First, the pspectra constituting the (N,N_(t))D GFT NMR experiment can be acquiredby successive omission of shift evolution periods from the ND FT NMRradiofrequency pulse scheme affording the basic spectra (Option 1).Alternatively, central peaks can be obtained from incompletepolarization transfer (Option 2) (Szyperski et al., J. Magn. Reson. B108:197-203 (1995), which is hereby incorporated by reference in itsentirety). The exclusive use of this approach corresponds to theirsimultaneous acquisition in the 2^(K) basic spectra. Alternatively,heteronuclear steady state magnetization can be recruited (Option 3)(Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996); Szyperski etal., J. Biomol NMR, 11:387-405 (1998), which are hereby incorporated byreference in there entirety). For each order of central peaks obtainedin such a way a recording of two subspectra is required so that thenumber of data sets increases twofold. The exclusive use of thisapproach would require recording of ₄ ^(K) different N_(t)D data sets.These yield, after data processing, the desired p=2^(K+1)−1 spectra.

[0186] Depending on the particular magnetization transfer pathway andpractical constraints, one can combine the three options for centralpeak detection. The second and third option offer that (i) magnetizationyielding unwanted “axial peaks” in the conventional experiment is used,(Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996), which ishereby incorporated by reference in its entirety) and that (ii) centralpeaks are registered even if the resonances in the higher-order spectraare broadened. Overall, 2^(K)<p<₄ ^(K) data sets thus need to berecorded to obtain the (N,N_(t))D GFT NMR experiment: the resulting“sampling demand” is equivalent to recording an ND FT NMR experimentwith only “one (2^(K) data sets) to two (₄ ^(K) data sets) complexpoints” in each of the K dimensions.

Example 3 Formula to Calculate the Reductions in Minimal MeasurementTimes for Different Options for Central Peak Acquisition

[0187] With respect to Option 1 for central peak acquisition (seeExample 2), if the p data sets defining the (N,N_(t))D experiment areseparately recorded, the ratio ε₁ is as defined in equation 3:$\begin{matrix}{{ɛ_{1} = {\frac{T_{m}({FT})}{T_{m}({GFT})} = {\left( {2^{K}/\left( {2^{K + 1} - 1} \right)} \right) \cdot {\left( {\prod\limits_{j = 0}^{K}\quad n_{j}} \right)/\left( {\sum\limits_{j = 0}^{K}n_{j}} \right)}}}},} & {(3),(10)}\end{matrix}$

[0188] With respect to Option 2 for central peak acquisition (seeExample 2), if the basic spectra are recorded with simultaneousacquisition of central peaks from incomplete INEPT, one obtains ε₂:$\begin{matrix}\begin{matrix}{ɛ_{2} = {\frac{T_{m}({FT})}{T_{m}({GFT})} = {\left( {2^{K + 1} \cdot {\prod\limits_{j = 0}^{K}n_{j}}} \right)/\left( {2^{K} \cdot 2 \cdot {\sum\limits_{j = 0}^{K}n_{j}}} \right)}}} \\{{= {\left( {\prod\limits_{j = 0}^{K}n_{j}} \right)/\left( {\sum\limits_{j = 0}^{K}n_{j}} \right)}},}\end{matrix} & (11)\end{matrix}$

[0189] i.e., the ratio becomes simply the product of the number ofpoints over the corresponding sum.

[0190] With respect to Option 3 for central peak acquisition (seeExample 2), if heteronuclear magnetization is exclusively used forcentral peak detection, one obtains ε₃: $\begin{matrix}{ɛ_{3} = {\frac{T_{m}({FT})}{T_{m}({GFT})} = {\left( {1/2^{K}} \right) \cdot {\left( {\prod\limits_{j = 0}^{K}n_{j}} \right)/{\left( {\sum\limits_{j = 0}^{K}n_{j}} \right).}}}}} & (12)\end{matrix}$

[0191] Table 1 illustrates the representative calculations of thereductions in minimal measurement times in GFT NMR. TABLE 1 TheReduction of Minimal Measurement Times, ε, for K = 1, 2, 3 and DifferentApproaches for Central Peak Detection Assuming That Each of theProjected K + 1 Dimensions are Sampled with 16(32) Complex Points 2^(K)basic data sets^(a) 2^(K+1) − 1 data sets^(b) 4^(K) data sets^(c)equation 11 equation 3 equation 12 K = 1 ε₂ = 8 (16) ε₁ = 5.3 (10.7) ε₃= 4 (8) K = 2 ε₂ = 85 (341) ε₁ = 48.6 (195) ε₃ = 21 (85) K = 3 ε₂ = 1024(8192) ε₁ = 546 (4369) ε₃ = 128 (1024)

[0192] For the implementation of (5,2)D HACACONHN , ¹³C^(α) steady statemagnetization was used to detect the first order central peaks definingthe Ω₁(¹H^(α)) splittings (see Examples 4 and 5), which yields a secondset of 8 data sets. Second and third order central peaks defining,respectively, the Ω₂(¹³C^(α)) and Ω₁(¹³C′) splittings were obtained fromseparate recording of somewhat higher resolved reduced-dimensionality(Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002);Szyperski et al. J. Biomol. NMR. 3:127-132 (1993); Szyperski et al., J.Am. Chem. Soc. 115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B105:188-191 (1994); Brutscher et al., J. Magn. Reson. B 105:77-82(1994); Szyperski et al., J. Magn. Reson. B 108:197-203 (1995);Brutscher et al., J. Magn. Reson. B 109:238-242 (1995); Szyperski etal., J. Am. Chem. Soc. 118:8146-8147 (1996); Bracken et al., J. Biomol.NMR 9:94-100 (1997); Szyperski et al., J. Biomol NMR, 11:387-405 (1998);Astrof et al., J. Magn. Reson. 152:303-307 (2001); Xia et al., J.Biomol. NMR 24:41-40 (2002), which are hereby incorporated by referencein their entirety). 2D HNNCO, an experiment derived from the HNNCOscheme (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, SanDiego (1996), which is hereby incorporated by reference in its entirety)(two data sets), and 2D [¹⁵N, ¹H]-HSQC (Ernst et al., Principles ofNuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford(1987), which is hereby incorporated by reference in its entirety),respectively (FIG. 16). The use of ¹³C^(α) steady-state magnetizationfor first order central peak detection yields ε=250 being intermediatebetween F (equation 3) and ε₃ (equation 12).

Example 4 NMR Spectroscopy

[0193] For the 76-residue protein ubiquitin nearly all signals of 2D[¹⁵N, ¹H]-HSQC (Ernst et al., Principles of Nuclear Magnetic Resonancein One and Two Dimensions, Clarendon, Oxford (1987), which is herebyincorporated by reference in its entirety) are resolved so that N_(t)=2is an obvious choice. As an application, a (5,2)D HACACONHN GFT NMRexperiment (K=3) was, thus, recorded within 138 minutes on a VARIANINOVA 600 spectrometer using the HACACONHN rf pulse sequence shown inFIG. 6. This experiment correlates the polypeptide backbone ¹H^(α),¹³C^(α) and ¹³C′ chemical shifts of residue i with the backbone amide¹⁵N and ¹H^(N) chemical shifts of residue i+1. The underlined lettersdenote that Ω₃(¹H^(α)), Ω₂(¹³C^(α)), Ω₁(¹³C′) and Ω₀(¹⁵N) are measuredin a single dimension. A 2 mM solution of ¹⁵N/¹³C doubly labeledubiquitin in 90% H₂O/10% D₂O (50 mM K—PO₄; pH=5.8) was used at T=25° C.

[0194] With the HACACONHN rf pulse scheme of FIG. 6, sixteen individualdata sets R1-R16 (to provide basic and first-order central peaks) wereacquired in 6.9 minutes each, with SW₁(¹⁵N/¹³C′/C¹³C^(α)/¹H^(α))=8,000Hz and 53(t₁)*512(t₂) complex points [t_(i,max)(¹⁵N/¹³C′/¹³C^(α/)¹H^(α))=6.5 ms; t₂ _(,max)(¹H^(N))=73.2 ms], yielding after dataprocessing (see Example 5) the twelve planes B1-B12 containing basic andfirst-order central peaks. The phase of the 90° rf pulses generatingtransverse ¹⁵N, ¹³C′, ¹³C^(α) and ¹H^(α) magnetization for frequencylabeling are φ₀, φ₁, φ₂, and φ₃, respectively (FIG. 6). φ₀ is alteredbetween 0° and 90° for phase sensitive acquisition (Ernst et al.,Principles of Nuclear Magnetic Resonance in One and Two Dimensions,Clarendon, Oxford (1987), which is hereby incorporated by reference inits entirety) of Ω₀(¹⁵N) along t₁. The three phases φ₁, φ₂ and φ₃ areindependently altered between 0° and 90° for frequency discrimination ofΩ₁(¹³C′), Ω₂(¹³C^(α)), and Ω₃(¹H^(α)) in the first eight data setsR1-R8. For first order central peak detection using ¹³C steady-statemagnetization (Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996);Szyperski et al., J. Biomol NMR, 11:387-405 (1998), which are herebyincorporated by reference in their entirety), the eight measurements arerepeated with the first 90° pulse on ¹H^(α) being shifted by 180°. Thisyields the following phase cycle for the 16 data sets R1-R16: φ₁=8(x,y); φ₂=4(2x, 2y); φ₃=4x, 4y, 4(−x), 4(−y) with the receiver phase beingunchanged. A reduced dimensionality (Szyperski et al., Proc. Natl. Acad.Sci. USA, 99:8009-8014 (2002); Szyperski et al., J. Am. Chem. Soc.115:9307-9308 (1993), which are hereby incorporated by reference intheir entirety) 2D HNNCO spectrum (second order central peaks) derivedfrom a HNNCO scheme (Cavanagh et al., Protein NMR Spectroscopy, AcademicPress, San Diego (1996), which is hereby incorporated by reference inits entirety) was acquired in 13.8 minutes with SW(¹⁵N/¹³C′)=8,000 Hzand 128(t₁)*512(t₂) complex points [t_(1,max)(¹⁵N/¹³C′)=15.9 ms;t_(2,max)(¹H^(N))=73.2 ms], yielding data sets R17 and R18 (B13 and B14after data processing; see Example 5) with phase φ₃=(x, y). A 2D [¹⁵N,¹H]-HSQC spectrum (Ernst et al., Principles of Nuclear MagneticResonance in One and Two Dimensions, Clarendon, Oxford (1987), which ishereby incorporated by reference in its entirety) (third order centralpeaks) was acquired in 13.8 minutes with SW(¹⁵N)=8,000 Hz, and256(t₁)*512(t₂) complex points [t_(1,max)(¹⁵N)=26 ms;t_(2,max)(¹H^(N))=73.2 ms], yielding the data set R19 (B15 after dataprocessing; see Example 5). For larger systems requiring longermeasurements, it might be advisable to derive second and third ordercentral peaks from ¹³C′ and ¹⁵N steady state magnetization,respectively. The total measurement time of the 19 data sets was 138minutes. To obtain pure phases, zero first-order phase corrections mustbe ensured along ω₁ by, for example, starting sampling at t₁=0 for allof the combined chemical shift evolution periods. Editing of chemicalshift multiplets in the time domain is advantageous, because theextension of the time domain data by linear prediction (Ernst et al.,Principles of Nuclear Magnetic Resonance in One and Two Dimensions,Clarendon, Oxford (1987), which is hereby incorporated by reference inits entirety) (from 53 to 106 complex points for data sets T1 to T12 andfrom 128 to 192 for data sets T13 and T14) profits from both maximizingthe signal-to-noise of the time domain data and reducing the number ofchemical shifts (“oscillators”) to be predicted. The digital resolutionafter FT and zero-filling was 7.8 Hz/point along ω₁ and 6.9 Hz/pointalong ω₂.

[0195] A 5D FT HACACONHN spectrum acquired with the same maximalevolution times as the basic spectra of (5,2)D HACACONHN would requiresampling of 10(t₁)*11(t₂)*22(t₃)*13(t₄)*512(t₅) complex points [i.e.,$\left\lbrack {{i.e.},{n = {\left( {\sum\limits_{j = 0}^{K}n_{j}} \right) - K}}} \right\rbrack$

[0196] with spectral widths of SW₁(¹⁵N)=1,440 Hz, SW₂(¹³C′)=1,500 Hz,SW₃(¹³C^(α))=3,260 Hz, and SW₄(¹H^(α))=1,800 Hz (i.e.,$\left( {{i.e.},{{SW} = {\sum\limits_{j = 0}^{K}{SW}_{j}}}} \right)$

[0197] in 5.83 days of spectrometer time. For comparison of digitalresolution in FT and GFT NMR, 2D [ω₁, ω₅]-, [ω₂, ω₅]-, [ω₃, ω₅]- and[ω₄, ω₅]-planes of the 5D FT HACACONHN experiment were recorded in 1.3,1.4, 2.9 and 1.7 minutes, respectively. For line width comparisons with(5,2)D GFT HACACONHN , the same planes were also acquired with spectralwidths of SW=8,000 Hz in the indirect dimension.

Example 5 Data Processing of the (5,2)D HACACONHN GFT NMR Spectrum

[0198] First order central peaks were derived from ¹³C steady statemagnetization. (Szyperski et al., J. Am. Chem. Soc. 118:8146-8147(1996); Szyperski et al., J. Biomol NMR, 11:387-405 (1998), which arehereby incorporated by reference in their entirety). This requires a“pre-processing” prior to G-matrix transformation. The data sets R1-R16are combined to yield the basic data sets, S1 . . . S8, and first ordercentral peak data sets, S9 . . . S12, respectively, according to:$\begin{matrix}{\begin{bmatrix}{S1} \\{S2} \\{S3} \\{S4} \\{S5} \\{S6} \\{S7} \\{S8}\end{bmatrix} = {\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1}\end{bmatrix} \cdot \begin{bmatrix}{R1} & \ldots & {R8} & {R9} & \ldots & {R16}\end{bmatrix}^{T}}} & (13) \\{and} & \quad \\{\begin{bmatrix}{S9} \\{S10} \\{S11} \\{S12}\end{bmatrix} = {\begin{bmatrix}0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0\end{bmatrix} \cdot {\begin{bmatrix}{R1} & \ldots & {R8} & {R9} & \ldots & {R16}\end{bmatrix}^{T}.}}} & (14)\end{matrix}$

[0199] This corresponds to the difference and sum formation for centralpeak acquisition using ¹³C^(α) steady state magnetization (Szyperski etal., J. Am. Chem. Soc. 118:8146-8147 (1996); Szyperski et al., J. BiomolNMR, 11:387-405 (1998), which are hereby incorporated by reference intheir entirety). Transverse ¹³C magnetization originating from ¹³Clongitudinal steady state magnetization is 90° out of phase relative totransverse ¹³C magnetization originating from ¹H magnetization.(Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996); Szyperski etal., J. Biomol NMR, 11:387-405 (1998), which are hereby incorporated byreference in their entirety). Hence, sin[Ω(¹³C)t] and cos[Ω(¹³C^(α))t]modulation are “swapped” for central peak acquisition and rows 1 and 2,and 3 and 4 in equation 14 are exchanged compared to equation 13. WithS13 and S14 from 2D HNNCO, and S15 from 2D [¹⁵N, ¹H]-HSQC, thep=2^(K+1)−1=15 data sets constituting the (5,2)D HACACONHN experimentbecome available. The required phase sensitive editing of the chemicalshift multiplet components can be achieved either in the frequency (seeExample 1) or the time domain (equation 1).

[0200] Ĝ_(c)(K), as defined by equation 1, can be decomposed into realand imaginary part, Ĝ_(c)(K)={circumflex over (R)}(K)+i·Î(K). With{circumflex over (R)}_(j)(K) and Î_(j)(K) denoting the correspondingj-th row vectors, one then obtains the real 2^(K+1)×2^(K+1) squareG-matrix, Ĝ(K)=[{circumflex over (R)}₁ Î₁ {circumflex over (R)}₂ Î₂ . .. Î₂ _(^(K)) Î₂ _(^(K)) ]^(T), which transforms Ŝ(K) into {circumflexover (T)}(K)=[T1r T1i T2r Tri . . . T2^(K)r T2^(K)i]^(T) according to{circumflex over (T)}(K)=Ĝ(K)·Ŝ(K). For time domain editing of the(5,2)D HACACONHN experiment, one thus obtains the following realG-matrices for K=3 (basic spectra): $\begin{matrix}{{\begin{bmatrix}{T1r} \\{T1i} \\{T2r} \\{T2i} \\{T3r} \\{T3i} \\{T4r} \\{T4i} \\{T5r} \\{T5i} \\{T6r} \\{T6i} \\{T7r} \\{T7i} \\{T8r} \\{T8i}\end{bmatrix} = {\begin{bmatrix}1 & 0 & 0 & {- 1} & 0 & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & 0 & {- 1} & 0 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 0 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 0 & {- 1} & {- 1} & 0 \\1 & 0 & 0 & 1 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 1 & 0 & {- 1} & 0 & 0 & {- 1} \\0 & 1 & {- 1} & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & {- 1} & 1 & 0 \\1 & 0 & 0 & {- 1} & 0 & 1 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 1 & 0 & 0 & {- 1} \\0 & 1 & 1 & 0 & {- 1} & 0 & 0 & 1 & 1 & 0 & 0 & {- 1} & 0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & {- 1} & 0 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 0 & 1 & 0 & 1 & {- 1} & 0 \\1 & 0 & 0 & {- 1} & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & {- 1} \\0 & 1 & 1 & 0 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 & 0 & {- 1} & 1 & 0 & 0 & 1 & {- 1} & 0 & 1 & 0 & 0 & 1 \\0 & 1 & {- 1} & 0 & 1 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 0 & 1 & {- 1} & 0 \\1 & 0 & 0 & {- 1} & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & {- 1} & 0 & 0 & 1 \\0 & 1 & 1 & 0 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & 0 & 1 & 0 & {- 1} & {- 1} & 0 \\1 & 0 & 0 & 1 & 0 & 1 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & {- 1} & 0 & 0 & {- 1} \\0 & 1 & {- 1} & 0 & {- 1} & 0 & 0 & {- 1} & {- 1} & 0 & 0 & {- 1} & 0 & {- 1} & 1 & 0\end{bmatrix} \cdot \begin{bmatrix}{S1r} \\{S1i} \\{S2r} \\{S2i} \\{S3r} \\{S3i} \\{S4r} \\{S4i} \\{S5r} \\{S5i} \\{S6r} \\{S6i} \\{S7r} \\{S7i} \\{S8r} \\{S8i}\end{bmatrix}}},} & (15)\end{matrix}$

[0201] for K=2 (first order central peaks): $\begin{matrix}{{\begin{bmatrix}{T9r} \\{T9i} \\{T10r} \\{T10i} \\{T11r} \\{T11i} \\{T12r} \\{T12i}\end{bmatrix} = {\begin{bmatrix}1 & 0 & 0 & {- 1} & 0 & {- 1} & {- 1} & 0 \\0 & 1 & 1 & 0 & 1 & 0 & 0 & {- 1} \\1 & 0 & 0 & 1 & 0 & {- 1} & 1 & 0 \\0 & 1 & {- 1} & 0 & 1 & 0 & 0 & 1 \\1 & 0 & 0 & {- 1} & 0 & 1 & 1 & 0 \\0 & 1 & 1 & 0 & {- 1} & 0 & 0 & 1 \\1 & 0 & 0 & 1 & 0 & 1 & {- 1} & 0 \\0 & 1 & {- 1} & 0 & {- 1} & 0 & 0 & {- 1}\end{bmatrix} \cdot \begin{bmatrix}{S9r} \\{S9i} \\{S10r} \\{S10i} \\{S11r} \\{S11i} \\{S12r} \\{S12i}\end{bmatrix}}},} & (16)\end{matrix}$

[0202] for K=1 (second order central peaks): $\begin{matrix}{{\begin{bmatrix}{T13r} \\{T13i} \\{T14r} \\{T14i}\end{bmatrix} = {\begin{bmatrix}1 & 0 & 0 & {- 1} \\0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 \\0 & 1 & {- 1} & 0\end{bmatrix} \cdot \begin{bmatrix}{S13r} \\{S13i} \\{S14r} \\{S14i}\end{bmatrix}}},} & (17)\end{matrix}$

[0203] and for K=0 (third order central peaks): $\begin{matrix}{\begin{bmatrix}{T15r} \\{T14i}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix} \cdot {\begin{bmatrix}{S15r} \\{S15i}\end{bmatrix}.}}} & (18)\end{matrix}$

[0204] Since real and imaginary parts are recorded for all four chemicalshifts Ω₀, Ω₁, Ω₂, and Ω₃ in the basic spectra (equation 15), theparticular choice of Ω₀ is, in principle, arbitrary. A suitablerearrangement of the FIDs allows one to exchange Ω₀ with any of theother three chemical shifts after data acquisition. However, the orderchosen for central peak detection defines Ω₀. For the (5,2)D HACACONHNexperiment, 2D [¹⁵N, ¹H]-HSQC is the most sensitive choice for thirdorder central peak detection so that Ω₀=Ω(¹⁵N).

Example 6 Peak Assignment and Calculation of Chemical Shifts

[0205] The chemical shift multiplets encoded in the edited spectra B1 .. . B15 of (5,2)D HACACONHN were identified starting from an assigned[¹⁵N, ¹H]-HSQC peak list in the “bottom-up” manner described in FIG. 3.The resulting peak lists of B1 . . . B15 were then used as input for aleast squares fitting routine (Eadie et al., Statistical Methods inExperimental Physics, North-Holland, N.Y. (1982); Lau, A NumericalLibrary in C for Scientists and Engineers, CRC Press, Boca Raton (1995),which are hereby incorporated by reference in their entirety) solving anoverdetermined system of 15 equations resulting from the Ω₁-frequenciesof the 15 peaks. This yielded the correlations involving Ω(¹H^(α) _(i)),Ω(¹³C^(α) _(i)), Ω(¹³C′_(i)), Ω(¹⁵N_(i+1)), and Ω(¹H^(N) _(i+1)) (Table2). A Monte Carlo simulation of error propagation (see description ofFIG. 19 for details) served to provide an estimate for the standarddeviations for the chemical shift measurements based on the measurementsof line widths. TABLE 2 Chemical Shifts^(a) of Ubiquitin Measured in (5,2)D HACACONHN. The Following Standard Deviations Were Obtained (FIGS.16-19); σ(¹⁵N) = ±0.043 ppm (2.4 Hz), σ(¹H^(N))^(b) = ±0.006 ppm (3.3Hz), σ(¹³C′) = ±0.017 ppm (2.6 Hz), σ(¹³C^(α)) = ±0.019 ppm (2.9 Hz),σ(¹H^(α)) = ±0.006 ppm (3.7 Hz). Residue δ(¹⁵N) δ(¹H^(N))^(a) δ(¹³C′)δ(¹³C^(α)) δ(¹H^(α)) M1 170.500 54.505 4.220 Q2 122.911 8.965 176.02155.178 5.289 I3 115.095 8.328 172.351 59.678 4.161 F4 118.498 8.624175.151 55.162 5.642 V5 121.256 9.317 174.775 60.430 4.815 K6 127.8478.954 177.095 54.682 5.293 T7 115.413 8.762 176.890 60.564 4.932 L8121.248 9.129 178.821 57.561 4.302 T9 105.850 7.656 175.494 61.463 4.423G10 109.192 7.845 173.952 45.428 3.612/4.344 K11 121.890 7.286 175.72256.318 4.359 T12 120.604 8.657 174.334 62.380 5.051 I13 127.688 9.562175.149 60.029 4.522 T14 121.650 8.757 173.731 62.043 4.977 L15 125.1508.751 174.525 52.827 4.754 E16 122.459 8.139 175.802 54.968 4.889 V17117.511 8.956 174.039 58.479 4.694 E18 119.306 8.679 P19 175.261 65.3304.124 S20 103.394 7.048 174.592 57.431 4.360 D21 123.869 8.070 176.28555.924 4.687 T22 108.971 7.895 176.760 59.658 4.905 I23 121.290 8.538E24^(c) 178.964 60.734 3.890 N25 121.406 7.942 178.288 56.068 4.558 V26122.156 8.118 177.918 67.684 3.398 K27 118.967 8.580 180.483 59.2224.592 A28 123.484 7.994 180.214 55.419 4.161 K29 120.211 7.875 180.25759.793 4.202 I30 121.352 8.301 178.151 66.124 3.487 Q31 123.551 8.568178.820 60.067 3.822 D32 119.733 8.036 177.278 57.454 4.333 K33 115.4327.446 177.777 58.193 4.310 E34 114.269 8.742 177.909 55.395 4.570 G35108.796 8.518 173.915 46.100 3.929/4.135 I36 120.298 6.174 P38 178.24666.138 4.116 D39 113.588 8.546 177.032 55.819 4.411 Q40 116.885 7.834175.381 55.647 4.463 Q41 118.029 7.498 176.133 56.684 4.223 R42 123.0338.524 173.854 55.186 4.483 L43 124.390 8.843 175.257 53.051 5.367 I44122.295 9.119 175.795 58.972 4.943 F45 125.055 8.866 174.578 56.5975.161 A46 132.938 8.993 177.317 52.598 3.697 G47 102.422 8.138 173.73245.412 3.450/4.100 K48 121.961 7.999 174.627 54.640 4.598 Q49 123.0008.664 175.566 55.922 4.540 L50 125.679 8.579 176.611 54.287 4.090 E51123.110 8.407 175.475 55.979 4.511 D52 120.354 8.179 G53^(c) 174.75445.245 4.062 R54 119.329 7.482 175.316 54.338 4.725 T55 108.815 8.847176.490 59.700 5.237 L56 118.016 8.168 180.752 58.673 4.053 S57 113.4848.499 178.282 61.149 4.242 D58 124.505 7.954 177.401 57.440 4.291 Y59115.770 7.276 174.663 58.295 4.651 N60 115.940 8.174 174.256 54.1794.351 I61 118.831 7.264 174.514 62.470 3.371 Q62 124.948 7.642 175.75153.653 4.477 K63 120.514 8.505 175.694 57.905 3.979 E64 114.574 9.335175.205 58.419 3.330 S65 114.914 7.683 172.008 60.931 4.632 T66 117.4398.742 173.741 62.506 5.291 L67 127.691 9.432 175.314 53.866 5.085 H68119.271 9.255 173.703 56.002 5.141 L69 123.921 8.311 175.356 53.8485.184 V70 126.737 9.202 174.033 60.654 4.378 L71 123.087 8.125 177.80654.030 5.021 R72 123.792 8.620 175.284 55.713 4.262 L73 124.533 8.372177.388 54.846 4.396 R74 121.936 8.453 176.837 56.613 4.303 G75 111.0898.505 173.633 45.331 3.966 G76 115.040 7.959

Example 7 Analysis of the (5,2)D HACACONHN GFT NMR Experiment

[0206] A (5,2)D HACACONHN GFT NMR experiment for the 8.6 kDa proteinubiquitin was acquired as an application of the GFT NMR spectroscopy.FIG. 16 shows the chemical shift multiplets as well as the resultingedited multiplet components, and FIG. 17 shows all 15 planesconstituting the (5,2)D HACACONHN experiment. The bottom upidentification (FIG. 3) of components forming a given shift multipletallows one to retain the 5D correlations of the parent experiment. Peakdetection was nearly complete so that a total of 67 chemical shift5-tuples as well as 3 shift 6-tuples for glycines with non-degenerate¹H^(α) shifts (Table 2) were obtained. The S/N ratios obtained in theGFT NMR experiment (The S/N ratios were between 6.4 and 12.0 in thebasic spectra (FIG. 17A), and between 5.6 and 10.4 for first-order peaks(FIG. 17B), between 9.8 and 24.0 for second-order peaks (FIG. 17C), andbetween 44.0 and 108.0 for third-order central peaks (FIG. 17D).)demonstrate adequate adjustment of the measurement time to sensitivityrequirements while the desired 5D chemical shift correlations wereregistered. The ratios also show that conventional 4D or 5D HACACONHNexperiments had to be acquired in the sampling limited data collectionregime because their minimal measurements are in the order of severaldays.

[0207] Because equivalent chemical shift correlations are provided by(5,2)D HACACONHN GFT and 5D HACACONHN FT NMR, these two experiments canbe compared in terms of minimal measurement times and data sizes. Anevident advantage of the GFT NMR experiment is the large reduction inT_(m). Equation 3 predicts reductions in measurement times of about anorder of magnitude for each dimension included into the joint samplingscheme (Table 1). In fact, the minimal measurement times with a singlescan per FID each second (and the same t_(max) for all chemical shiftevolution periods as chosen for basic and first order central peakacquisition) are 33.5 min. and 5.83 days for (5,2)D HACACONHN GFT NMR(FIG. 17) and 5D HACACONHN FT NMR, revealing a 250-fold reduction inT_(m)for the GFT experiment (note that this value deviates from ε=317obtained with equation 2, due to the particular choice to implementcentral peak acquisition; see Example 3). Concomitantly, the data sizeis largely reduced when transformed data sets with equal digitalresolution are compared (FIG. 18).

[0208] In order to assess the precision of the chemical shiftmeasurements the resonance line widths need to be considered (Ernst etal., Principles of Nuclear Magnetic Resonance in One and Two Dimensions,Clarendon, Oxford (1987), which is hereby incorporated by reference inits entirety). In general, the joint sampling of K+1 “non constant-time”chemical shift evolution periods yields transfer amplitudes attenuatedby${\exp \left( {- {\sum\limits_{j = 0}^{K}{R_{2,j} \cdot t}}} \right)},$

[0209] where R_(2J) represents the transverse relaxation rate constantof the j-th dimension. However, higher-dimensional heteronuclear FT NMRshift correlation spectra are quite often recorded with frequencylabeling being accomplished in a constant-time manner (Cavanagh et al.,Protein NMR Spectroscopy. Academic Press, San Diego (1996), which ishereby incorporated by reference in its entirety) and/or witht_(j,max)<<1/R_(2,j) for all j. As for the implementation of (5,2)DHACACONHN, the linewidth is then determined by the t_(max) values but isnot dependent on R_(2j). Assuming for simplicity that all t_(j,max) areidentical, the 2^(K) lines of the chemical shift multiplets exhibit thesame width as the corresponding single peak in ND FT NMR along each ofthe dimensions. Hence, peaks are not broadened in constant-time GFT NMRspectra with increasing K (The width at half height of the frequencydomain sinc centre lobe resulting from truncation in the time domain att_(max) is given² by 0.604/t_(max). In the current implementation of(5,2)D HACACONHN (FIG. 6) all indirect evolution periods except forΩ(¹H^(α)) are constant time periods. The evolution of Ω(¹H^(α)) isimplemented in a semi constant time manner (Cavanagh et al., Protein NMRSpectroscopy. Academic Press, San Diego (1996), which is herebyincorporated by reference in its entirety), so that signal losses due totransverse relaxation of ¹H^(α) are negligible for 8.6 kDa ubiquitin atshort t_(max) values around 6.5 ms. For larger systems with shortT₂(¹H^(α)), however, the semi constant time frequency labeling may leadto a detectable increase of ω₁-linewidths in the basic when compared tocentral peak spectra.) This is neatly confirmed when comparing sol crosssections from (5,2)D HACACONHN with those taken from 2D HACACONHNspectra (FIGS. 18A-B).

[0210] The fact that the individual multiplet components possess thesame line widths as the corresponding signals in the parent FT NMRexperiment (FIGS. 18A-B) has a profound impact on the precision of thechemical shift measurement in constant time GFT NMR experiments such as(5,2)D HACACONHN. To relate line widths to errors of measurement, aconservative statistical model was adopted in which (i) the error forthe identification of peak positions is associated with a Gaussiandistribution and (ii) the Lorenzian line width, Δν_(1/2), represents thecorresponding 99.5% confidence interval (i.e., Δν_(1/2)=6σ). σ(basic),σ(first), σ(second) and σ(third) are the standard deviations for shiftmeasurements in basic, first order, second order and third order centralpeak spectra, respectively. Considering (i) that lines do not broadenwith increasing K (FIGS. 18A-B) and (ii) the different maximal evolutiontimes (see Example 4), one has thatσ(basic)=σ(first)=σ^(FT)(¹³C^(α))=σ^(FT)(¹H^(α)), σ(second)=σ^(FT)(¹³C′)and σ(third)=σ^(FT)(¹⁵N). σ^(FT)(X) represents the standard deviationfor the chemical shift measurement of nucleus X (¹H^(α), ¹³C^(α), ¹³C′,¹⁵N) in conventional FT NMR spectra acquired with corresponding t_(max).Monte Carlo simulations were performed to calculate the standarddeviations σ(¹³C^(α)), σ(¹H^(α)), σ(¹³C′), and σ(¹⁵N) in (5,2)DHACACONHN GFT NMR for various selections of subspectra (FIGS. 19-20). Ifa minimal number of four basic spectra is selected to calculateΩ₃(¹H^(α)), Ω₂(¹³C^(α)), σ₁(¹³C′) and Ω₀(¹⁵N), the precision depends onwhich four are selected (see FIG. 20 and its description for details).In the two most favorable cases, the standard deviations in the constanttime GFT NMR experiment are reduced by a factor of 2={squareroot}{square root over (4)}, that is,${\sigma (X)} = {{\frac{1}{2}{\sigma^{FT}\left( {{}_{}^{}{}_{}^{}} \right)}} = {{\frac{1}{2}{\sigma^{FT}\left( {{}_{}^{}{}_{}^{}} \right)}} = {\frac{1}{2}{{\sigma ({basic})}.}}}}$

[0211] If the 8 basic spectra are selected, the standard deviation isreduced by an additional factor of {square root}{square root over (2)},yielding${\sigma (X)} = {\frac{1}{\sqrt{8}} \cdot {{\sigma ({basic})}.}}$

[0212] Similarly,${\sigma (X)} = {\frac{1}{\sqrt{12}} \cdot {\sigma ({basic})}}$

[0213] if both the 8 basic and 4 first order central peak spectra arechosen. The exact match between reductions by a factor of {squareroot}{square root over (n)}, where n represents the number of spectra,and the reductions obtained from the simulations (see descriptions ofFIGS. 19-20 for details) reflects the well-known relation fromstatistics (Eadie et al., Statistical Methods in Experimental Physics,North-Holland, N.Y. (1982), which is hereby incorporated by reference inits entirety) stating that the standard deviation of an average arisingfrom n multiple independent measurements is reduced by a factor of{square root}{square root over (n)} (FIG. 1). For the implementation of(5,2)D HACACONHN, second- and third-order central peak spectra wereacquired with longer maximal evolution times than the first-ordercentral peak and basic spectra (FIG. 17E; see Example 4). Hence, σ(¹³C′)and σ(¹⁵N) turned out to be somewhat smaller than${{\frac{1}{\sqrt{14}} \cdot {\sigma ({basic})}}\quad {and}\quad {\frac{1}{\sqrt{15}} \cdot {\sigma ({basic})}}},$

[0214] respectively, when 14 or all 15 spectra are considered (seedescription of FIG. 20 for details). When compared withσ(second)=σ^(FT)(¹³C′) and σ(third)=σ^(FT)(¹⁵N), which reflect ratherlong maximal evolution times, the values of σ(¹³C′) and σ(¹⁵N) arereduced by factors of 2.5 and 2.0, respectively. The Monte Carlosimulations are in neat agreement with analytical calculations ofstandard deviations using the Gaussian law of error propagation (Eadieet al., Statistical Methods in Experimental Physics, North-Holland, N.Y.(1982), which is hereby incorporated by reference in its entirety) (seedescription of FIG. 20) and are evidently a valuable tool to analyze theprecision of shift measurements in more intricate future implementationsof GFT NMR experiments.

[0215] Overall, the precision of the indirect shift measurements in the(5,2)D HACACONHN experiment [σ(¹H^(α))=3.7 Hz, σ(¹³C^(α))=2.9 Hz,σ(¹³C′)=2.6 Hz, σ(¹⁵N)=2.4 Hz] matched the one obtained in the directdimension [σ(¹H^(N))=3.3 Hz]. Remarkably, one can anticipate formolecules tumbling slower than ubiquitin at 25° C, that the precision ofthe indirectly detected shifts will be higher than for the directlydetected amide proton shift. This is because the precision of shiftmeasurements in the indirect constant-time evolution periods isdetermined by t_(max) (which would not change for larger proteins),while the precision in the direct dimension is decreasing withincreasing R_(2,HN).

Example 8 Analytical Calculations Using the Gaussian Law of ErrorPropagation

[0216] Three different classes of combinations are identified.

[0217] (I) 2 combinations provide high precision$\left\lbrack {{\sigma (X)} = {\frac{1}{2} \cdot}} \right.$

[0218] σ(basic); X=¹H^(α), ¹³C^(α), ¹³C′, ¹⁵N] for all four chemicalshifts:

B1[Ω₀+Ω₁+Ω₂+Ω₃ ]; B4[Ω₀−Ω₁−Ω₂+Ω₃ ]; B6[Ω₀−Ω₁+Ω₂−Ω₃]; and

B7[Ω₀+Ω₁−Ω₂−Ω₃], or

B2[Ω₀−Ω₁+Ω₂+Ω₃ ]; B3[Ω₀+Ω₁−Ω₂+Ω₃ ]; B5[Ω₀+Ω₁+Ω₂−Ω₃]; and

B8[Ω₀−Ω₁−Ω₂−Ω₃].

[0219] (II) 26 combinations provide intermediate precision$\left\lbrack {{\sigma (X)} = {\frac{1}{\sqrt{2}} \cdot}} \right.$

[0220] σ(basic); X=¹H^(α), ¹³C^(α,) ¹³C′, ¹⁵N] for all four chemicalshifts.

[0221] (III) 37 combinations provide intermediate precision$\left\lbrack {\sigma = {\frac{1}{\sqrt{2}} \cdot}} \right.$

[0222] σ(basic)] for three of the shifts and low precision [σ=σ(basic)]for one of the four shifts.

[0223] The standard deviation depends on the number of equations thatneed to be linearly combined to calculate the shifts. This can bediscussed for three examples, one representing each of the cases.

[0224] (I) B2[Ω₀−Ω₁+Ω₂+Ω₃]; B3[Ω₀+Ω₁−Ω₂+Ω₃]; B5[Ω₀+Ω₁+Ω₂−Ω₃]; andB8[Ω₀−Ω₁−Ω₂−Ω₃] are selected. Then, the individual chemical shifts areobtained from:

4Ω₀(¹⁵N)=B2+B3+B5+B8

4Ω₁(¹³C′)=−B2+B3+B5−B8

4Ω₂(¹³C^(α))=B2−B3+B5−B8

4Ω₃(¹H^(α))=B2+B3−B5−B8

[0225] with “BX” representing the shifts extracted from the spectrum BX(X=2,3,5,8). Each shift from BX is associated with a standard deviationof σ(basic) Hence, the Gaussian law of error propagation (Eadie et al.,Statistical Methods in Experimental Physics, North-Holland, N.Y. (1982),which is hereby incorporated by reference in its entirety) yields:

σ[4Ω₀(¹⁵N)]=4σ[Ω₀(¹⁵N)]={square root}{square root over(4)}σ(basic)=2·σ(basic)

σ[4Ω₀(¹³C′)]=4σ[Ω₀(¹³C′)]={square root}{square root over(4)}σ(basic)=2·σ(basic)

σ[4Ω₀(¹³C^(α))]=4σ[Ω₀(¹³C^(α))]={square root over(4)}σ(basic)=2·σ(basic)

σ[4Ω₀(¹H^(α))]=4σ[Ω₀(¹H^(α))]={square root}{square root over(4)}σ(basic)=2·σ(basic),

[0226] or equivalently,${\sigma \left\lbrack {\Omega_{0}(X)} \right\rbrack} = {{\frac{1}{\sqrt{4}}{\sigma ({basic})}} = {\frac{1}{2} \cdot \sigma}}$

[0227] (basic) for X=¹H^(α), ¹³C^(α), ¹³C′, ¹⁵N.

[0228] Thus, the resulting precision is equivalent to the one obtainedfrom four statistically independent measurements.

[0229] (II) B1[Ω₀+Ω₁+Ω₂+Ω₃]; B5[Ω₀+Ω₁+Ω₂−Ω₃]; B7[Ω₀+Ω₁−Ω₂−Ω₃]; and B8[Ω₀−Ω₁−Ω₂−Ω₃] are selected. Then, the individual chemical shifts areobtained from:

2[Ω₀(¹⁵N)=B1+B8

2Ω₁(¹³C′)=B7−B8

2Ω₂(¹³C^(α))=B5−B7

2Ω₃(¹H^(α))=B1−B5

[0230] with “BX” representing the shifts extracted from the spectrum BX(X=1,5,7,8). Each shift from BX is associated with a standard deviationof σ(basic). Hence, the Gaussian law of error propagation yields:

σ[2Ω₀(¹⁵N)]=2σ[Ω₀(¹⁵N)]={square root}{square root over (2)}σ(basic)

σ[2Ω₀(¹³C′)]=2σ[Ω₀(¹³C′)]={square root}{square root over (2)}σ(basic)

σ[2Ω₀(¹³C^(α))]=2σ[Ω₀(¹³C^(α))]={square root}{square root over(2)}σ(basic)

σ[2Ω₀(¹H^(α))]=2σ[Ω₀(¹H^(α))]={square root}{square root over(2)}σ(basic),

[0231] or equivalently,${\sigma \left\lbrack {\Omega_{0}(X)} \right\rbrack} = {\frac{1}{\sqrt{2}}{\sigma ({basic})}}$

[0232] for X=¹H^(α), ¹³C^(α), ¹³C′, ¹⁵N.

[0233] Thus, the resulting precision is equivalent to the one obtainedfrom two statistically independent measurements.

[0234] (III) B1[Ω₀+Ω₁+Ω₂+Ω₃]; B4[Ω₀−Ω₁−Ω₂+Ω₃]; B5[Ω₀+Ω₁+Ω₂−Ω₃]; andB6[Ω₀−Ω₁+Ω₂−Ω₃] are selected. Then, the individual chemical shifts areobtained from:

2[Ω₀(¹⁵N)=B4+B5

2Ω₁(¹³C′)=B5−B6

2Ω₂(¹³C^(α))=B1−B4−B5+B6

2Ω₃(¹H^(α))=B1−B5

[0235] with “BX” representing the shifts extracted from the spectrum BX(X=1,4,5,6). Each shift from BX is associated with a standard deviationof σ(basic). Hence, the Gaussian law of error propagation yields:

σ[2Ω₀(¹⁵N)]=2σ[Ω₀(¹⁵N)]={square root}{square root over (2)}σ(basic)

σ[2 Ω₀(¹³C′)]=2σ[Ω₀(¹³C′)]={square root}{square root over (2)}σ(basic)

σ[2Ω₀(¹³C^(α))]=2σ[Ω₀(¹³C^(α))]={square root}{square root over(4)}σ(basic)=2·σ(basic)

σ[2Ω₀(¹H^(α))]=2σ[Ω₀(¹H^(α))]={square root}{square root over(2)}σ(basic)

[0236] or equivalently,${\sigma \left\lbrack {\Omega_{0}(X)} \right\rbrack} = {\frac{1}{\sqrt{2}}{\sigma ({basic})}}$

[0237] for X=¹H^(α), ¹³C′, ¹⁵N and σ[Ω₀(¹³C^(α))]=σ(basic)

[0238] Thus, the resulting precision is equivalent to the one obtainedfrom two statistically independent measurements for three of thechemical shifts, while it is equivalent to a single measurement for oneof the shifts.

[0239] In case all 15 spectra constituting the constant time (5,2)D GFTNMR experiment are selected, similar considerations show that theresulting standard deviations can be calculated (Eadie et al.,Statistical Methods in Experimental Physics, North-Holland, N.Y. (1982),which is hereby incorporated by reference in its entirety) according tothe following equations.

[0240] (a) Survey of constant time spectra, standard deviations andchemical shift measurements Number of Standard Data Spectra DeviationChemical Shift Measurements Basic 8 σ(basic) Ω₀(¹⁵N) ± Ω₁(¹³C′) ±Ω₂(¹³C^(α)) ± Ω₃(¹H^(α)) 1st 4 σ(1st) Ω₀(¹⁵N) ± Ω₁(¹³C′) ± Ω₂(¹³C^(α))2nd 2 σ(2nd) Ω₀(¹⁵N) ± Ω₁(¹³C′) 3rd 1 σ(3rd) Ω₀(¹⁵N)

[0241] (b) Calculation of error propagation Chemical Shifts StandardDeviations Ω₀(¹⁵N)${\sigma \left( {}^{15}N \right)} = \frac{\sqrt{{8 \cdot {\sigma^{2}({basic})}} + {4 \cdot {\sigma^{2}\left( {1{st}} \right)}} + {2 \cdot {\sigma^{2}\left( {2{nd}} \right)}} + {\sigma^{2}\left( {3{rd}} \right)}}}{15}$

Ω₁(¹³C′)${\sigma \left( {}^{15}C^{\prime} \right)} = \frac{\sqrt{{8 \cdot {\sigma^{2}({basic})}} + {4 \cdot {\sigma^{2}\left( {1{st}} \right)}} + {2 \cdot {\sigma^{2}\left( {2{nd}} \right)}}}}{14}$

Ω₂(¹³C^(α))${\sigma \left( {}^{15}C^{\alpha} \right)} = \frac{\sqrt{{8 \cdot {\sigma^{2}({basic})}} + {4 \cdot {\sigma^{2}\left( {1{st}} \right)}}}}{12}$

Ω₃(¹H^(α))${\sigma \left( {}^{1}H^{\alpha} \right)} = \frac{\sqrt{8 \cdot {\sigma^{2}({basic})}}}{8}$

[0242] The validity of these equations is neatly confirmed by the MonteCarlo simulation performed with input from all 15 spectra: σ 6σ(simulated) 6σ (calculated) σ(¹⁵N) 14.50 14.46 σ(¹³C′) 15.35 15.37σ(¹³C^(α)) 17.41 17.36 σ(¹H^(α)) 21.24 21.26

Example 9 Implementation of the (5,2)D HACA,CONHN, (5,3)DHACA,CONHN/(5,3)D HACACONHN, and (4,3)D CBCACONHN/(4,3)D CBCA,CONHN GFTNMR Experiments

[0243] The following GFT NMR experiments were implemented (FIG. 4): (i)with K=3, (5,2)D HACA,CONHN complementing (5,2)D HACACONHN forsequential assignment, (ii) with K=2, (5,3)D HACA,CONHN and (5,3)DHACACONHN, where, in contrast to the (5,2)D experiments in (i), the ¹⁵Nchemical shifts evolve separately, and (iii) with K=1, (4,3)D CBCACONHNand (4,3)D CBCA,CONHN. The underlined letters indicate which chemicalshifts that are jointly sampled. After G-matrix transformation oneobtains 2³⁺¹−1=15 2D planes for the (5,2)D experiments (K=3), seven 3Dspectra for the (5,3)D experiments (K=2) and three 3D spectra for the(4,3)D experiments (K=1). The magnetization transfer pathways aredepicted in FIGS. 4A-C. Spectra were acquired for the 8.6 kDa proteinubiquitin and for the 14 kDa protein TT212 from the protein structureproduction pipeline of the Northeast Structural Genomics Consortium(http://www.nesg.org, which is hereby incorporated by reference in itsentirety).

[0244] (5,2)D HACA,CONHN/(5,2)D HACACONHN and (5,3)D HACA,CONHN/(5,3)DHACACONHN correlate the backbone amide ¹⁵N and ¹HN chemical shifts ofresidue i with the ¹³C′, ¹³C^(α) and ¹H^(α) chemical shifts of residuei−1 and i, respectively, via one-bond scalar couplings (FIGS. 4A-B). Inaddition, the often smaller two-bond scalar couplings between the¹⁵N_(i) and ¹³C^(α) _(i−1), may yield sequential connectivities in theHACA,CONHN experiments. The comma separating “CA” from “CO” indicatesthat the intraresidue ¹³C′ chemical shift is obtained by creatingtwo-spin coherence involving ¹³C^(α) and ¹³C′ during the intraresiduepolarization transfer from ¹³C^(α), to ¹⁵N (Löhr et al., J. Biomol. NMR6:189-197 (1995), which is hereby incorporated by reference in itsreference). The (5,2)D HACA,CONHN experiment was recorded with theradio-frequency (rf) pulse scheme of FIG. 7A. Löhr et al., J. Biomol.NMR 6:189-197 (1995), which is hereby incorporated by reference in itsentirety, can be referred to for a product operator description of theexperiment. Since rf pulses on ¹³C′ are employed as laminar shiftedpulses (Cavanagh et al., Protein NMR Spectroscopy, Wiley, N.Y. (1996),which is hereby incorporated by reference in its entirety), the spectralwidth of the indirect dimension was set to one half of the difference ofthe ¹³C^(α) and ¹³C′ carrier frequencies (8,897 Hz at 600 MHz) in orderto fold the ¹³C′ onto the ¹³C^(α) carrier frequency. In the currentimplementation of (5,2)D HACA,CONHN, Ω(¹⁵N) was detected in quadraturein the GFT dimension ω₁. With the GFT NMR super phase-cycle given in thelegend of FIG. 7A, this yields (i) eight basic 2D spectra with peaks atΩ₀(¹⁵N)±Ω₁(¹³C′)±Ω₂(¹³C^(α))±Ω₃(¹H^(α)) along ω₁, (ii) four 2D firstorder central peak spectra with peaks at Ω₀(¹⁵N)±Ω₁(¹³C′)±Ω₂(¹³C^(α)),(iii) two 2D second order central peak spectra with peaks atΩ₀(¹⁵N)±Ω₁(¹³C′) and (iv) one 2D third order central peak spectrum withpeaks at Ω₀(¹⁵N). The choice for the order of central peak detection isprimarily guided by sensitivity considerations. First order centralpeaks were derived from ¹³C^(α) magnetization, which allows one todetect these central peaks while the basic spectra are acquired. Hence,when the basic spectra are acquired with at least two scans perincrement, the first order central peaks are obtained from ¹³C steadystate magnetization without investment of additional measurement time.In case single scan acquisition is chosen for the basic spectra, firstorder central peak detection would be best implemented by simplyomitting the ¹H^(α) shift evolution. Second order central peak werederived from ¹H^(α) magnetization using the scheme of FIG. 7A, i.e., byomitting both the ¹H^(α) and ¹³C^(α) chemical shift evolution periods.This approach is more sensitive than using 2D HNN(CA)CO. Finally,sensitive 2D [¹⁵N, ¹H]-HSQC provided the third order central peaks. Tomatch (5,2)D HACA,CONHN, (5,2)D HACACONHN (FIG. 4A) was acquired withthe same order for central peak detection as in (5,2)D HACA,CONHN,except that the spectral width of the indirect GFT dimension was set to8,897 Hz.

[0245] (5,3)D HACACONHN and HACA,CONHN were recorded using the pulsescheme and a correspondingly reduced GFT NMR super phase cycle of the(5,2)D congeners (FIG. 7A); Ω(¹³C′) was detected in quadrature in theGFT dimension and Ω(¹⁵N) was sampled in a separate chemical shiftevolution along ω₂. This yields (i) four basic 3D spectra with peaks atΩ₀(¹³C′)±Ω₁(¹³C^(α))±Ω₂(¹H^(α)), (ii) two first order central peakspectra with peaks at Ω₀(¹³C′)±Ω₁(¹³C^(α)) and (ii) one second ordercentral peak spectrum with peaks at Ω₀(¹³C′).

[0246] (4,3)D CBCACONHN and (4,3)D CBCA,CONHN correlate the backboneamide ¹⁵N and ¹HN chemical shifts of residue i with the ¹³C′, ¹³C^(α)and ¹³C^(β) chemical shifts of residue i−1 and i, respectively, viaone-bond scalar couplings (FIG. 4C), and the often smaller two-bondscalar couplings between the ¹⁵N_(i) and ¹³C^(α) _(i−1) may yieldadditional sequential connectivities in (4,3)D CBCA,CONHN. Ω(¹³C′) wasdetected in quadrature in the GFT dimension thus yielding (i) two basic3D spectra with peaks at Ω₀(¹³C′)±Ω₁(¹³C^(α)) and Ω₀(¹³C′)±Ω₁(¹³C^(β))and (ii) one central peak spectrum with peaks at Ω₀(¹³C′). (4,3)DCBCACONHN was recorded by modifying the H^(α/β)C^(α/β)(CO)NHN pulsescheme (derived from CBCA(CO)NHN; Grzesiek et al., J. Am. Chem. Soc.114:6291-6293 (1992), which is hereby incorporated by reference in itsentirety) described in Szyperski et al., Proc. Natl. Acad. Sci. USA99:8009-8014 (2002), which is hereby incorporated by reference in itsentirety: the ¹H^(α/β) chemical shift evolution was eliminated and a¹³C′ chemical shift evolution was introduced in a constant-time manner(see FIG. 8 for the rf pulse scheme). (4,3)D CBCA,CONHN was recordedwith the new pulse scheme shown in FIG. 7B, that is, ¹³C′-¹³C^(α)two-spin coherence is created for simultaneous ¹³C′ and ¹³C^(α)frequency labeling during the polarization transfer from ¹³C′ to ¹⁵N.

Example 10 Analyses of the (5,2)D HACA,CONHN, (5,3)D HACA,CONHN/(5,3)DHACACONHN, and (4,3)D CBCACONHN/(4,3)D CBCA,CONHN GFT NMR Experiments

[0247] On a VARIAN Inova 600 MHz spectrometer at 25° C, (i) (5,2)DHACACONHN (2.5 hrs. measurement time), (5,2)D HACA,CONHN (8.1 hrs.),(ii) (5,3)D HACACONHN (10.4 hrs.) and (5,3)D HACA,CONHN (10.4 hrs.), and(iii) (4,3)D CBCACONHN (5.6 hrs.) and (4,3)D CBCA,CONHN (5.6 hrs.) wereacquired for a 2 mM solution (pH=5.8, 50 mM K—PO₄, 90% H2O/10% D₂O) ofthe 8.6 kDa protein ubiquitin. (5,3)D HACACONHN (20.8 hrs.) and (5,3)DHACA,CONHN (41.8 hrs) were also acquired for a 1 mM solution (pH=6.5,450 mM NaCl, 10 mM DTT, 20 mM Zn²⁺, 0.01% NaN₃, 95% H₂O/5% D₂O) of the14 kDa protein structural genomics target protein TT212.

[0248] The yield of peak detection, i.e. the ratio of observed peaksover the total number of expected peaks, was (virtually) completethroughout. Reductions in minimal measurement time, ε, achievable in GFTNMR are given by the ratio of the number of free induction decays (FIDs)of an (N,N—K)D GFT NMR experiment over and the number FIDs of the ND FTNMR experiment.

[0249] For ubiquitin, the following was obtained: (i) (5,2)D HACACONHN(ε=225; 100% yield; S/N for peaks in basic spectra: 6.9-14.8; in firstorder central peak spectra: 8.1-10.4), (5,2)D HACA,CONHN (ε=225;intraresidue correlations: 100% yield; S/N for peaks in basic spectra:4.0-6.8; in first order central peak spectra: 3.3-5.3), (ii) (5,3)DHACACONHN (ε=25; 100% yield; S/N for peaks in basic spectra: 27.5-61.2;in first order central peak spectra: 26.2-41.3) and (5,3)D HACA,CONHN(ε=25; intraresidue correlations: 100% yield; S/N for peaks in basicspectra: 14.7-23.6; 93% in first order central peak spectra: 13.1-22.6),(iii) (4,3)D CBCA,CONHN (ε=6.4; ¹³C^(α) correlations in basic spectra:100% yield; S/N: 31.1-72.3; ¹³C^(β) correlations in basic spectra: 100%yield; S/N: 23.8-81.1) and (4,3)D CBCA,CONHN (ε=6.4; intraresidue¹³C^(α) correlations in basic spectra: 100% yield; S/N: 3.7-23.9;intraresidue ¹³C^(β) correlations in basic spectra: 99% yield; S/N:2.7-9.7).

[0250] For TT212, the following was obtained: (5,3)D HACACONHN (6=25;100% yield; S/N for peaks in basic spectra: 3.0-44.6; in first ordercentral peak spectra: 2.5-34.4) and (5,3)D HACA,CONHN (ε=25;intraresidue correlations: 96% yield; S/N for peaks in basic spectra:1.5-14.0; 93% in first order central peak spectra: 1.5-14.7). (S/Nratios not reported for other central peak spectra are larger than thoseof the first order central peaks.)

[0251] When using (5,2)D HACACONHN/HACA,CONHN (FIG. 21) or (5,3)DHACACONHN and HACA,CONHN (FIG. 22), the sequential assignment is basedon the three chemical shifts Ω(¹³C′),Ω(¹³C^(α)) and Ω(¹H^(α)). The useof(4,3)D CBCACONHN/(4,3)D CBCA,CONHN (FIG. 23) corresponds to having two4D experiments in which the number of correlations is increased by a¹³C^(β)-¹³C^(α) relay step. Hence, the (4,3)D experiments likewiseprovide assignments based on three chemical shifts, i.e.Ω(¹³C′),Ω(¹³C^(α)) and Ω(¹³C^(β)). Note, however, that Ω(¹³C^(α)) andΩ(¹³C^(β)) of a given residue are not directly correlated. FIGS. 21-23show that the exhaustive sampling of linear combinations of chemicalshifts yields an extended set of sequential connectivities when comparedwith conventional FT NMR. For example, in (5,3)D HACACONHN/HACA,CONHNseven peaks located at Ω₀(¹³C′)±Ω₁(¹³C^(α))±Ω₂(¹H^(α)) (spectra B1 to B4in FIG. 22), Ω₀(¹³C′)±Ω₁(¹³C^(α)) (spectra B5 and B6 in FIG. 22) andΩ₁(¹³C′) (spectrum B7 in FIG. 22) serve as sequential matchingconstraints. Recording of 3D HA(CACO)NHN, 3D (HA)CA(CO)NHN and 3D(HACA)CONHN spectra in conjunction with their intraresidue counterpartswould yield only 3 constraints, which are devoid of direct correlationsbetween the shifts of ¹³C′, ¹³C^(α) and ¹H^(α) (as provided by the(5,3)D GFT NMR experiment).

[0252] Furthermore, the experimental error of chemical shiftmeasurements in constant time GFT NMR experiments scales with 1/({squareroot}{square root over (n)}), where n is the number of linearcombinations contributing to the determination of a shift (assuming, forsimplicity, that the same maximal evolution times have been chosen). Theincreased accuracy of the measurement is documented by comparing theshifts of the same nuclei measured in intra- and interresidue GFT data.Tables 3 to 5 afford a detailed analysis of the shift measurementsassociated with sequential connectivities shown in FIGS. 21 to 23,respectively. These tables provide both the measured linear combinationsof shifts and the single-quantum shifts obtained from a linearleast-squares fit. The experimental errors for the measurement of thelinear combinations of the chemical shifts were estimated as describedabove. The comparison of shifts for the same nucleus as obtained fromtwo different GFT NMR spectra shows that the accuracy is indeed high:the shift differences in Tables 3 to 5 (underlined values; see alsoTable 6 with the shift analysis corresponding to FIG. 24) are smallerthan 0.081 ppm for all cases in (5,3)D and (5,2)D GFT NMR spectra, andsmaller than 0.154 ppm in the (4,3)D spectra. TABLE 3 Chemical ShiftsMeasured in (5,2)D HACA,CONHN/ (5,2)DHACACONHN Recorded for Ubiquitin(see FIG. 21). The Underlined Values in the Lower Right Represent theDifferences of Single-Quantum Shifts Obtained from (5,2)D HACA,CONHN and(5,2)D HACACONHN. (A) (5,2)D HACA,CONHN Linear combinations of shifts(Glu 64) measured along ω₁ [ppm] Ω₀(¹⁵N) + Ω₁(¹³C′) + Ω₂(¹³C^(α)) +Ω₃(¹H^(α)) 108.075 ± 0.167 B1 Ω₀(¹⁵N) − Ω₁(¹³C′) + Ω₂(¹³C^(α)) +Ω₃(¹H^(α)) 103.697 ± 0.167 B2 Ω₀(¹⁵N) + Ω₁(¹³C′) − Ω₂(¹³C^(α)) +Ω₃(¹H^(α))  97.120 ± 0.167 B3 Ω₀(¹⁵N) − Ω₁(¹³C′) − Ω₂(¹³C^(α)) +Ω₃(¹H^(α))  92.937 ± 0.167 B4 Ω₀(¹⁵N) + Ω₁(¹³C′) + Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 136.303 ± 0.167 B5 Ω₀(¹⁵N) − Ω₁(¹³C′) + Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 131.989 ± 0.167 B6 Ω₀(¹⁵N) + Ω₁(¹³C′) − Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 125.512 ± 0.167 B7 Ω0(¹⁵N) − Ω1(¹³C′) − Ω2(¹³C^(α)) −Ω3(¹H^(α)) 121.182 ± 0.167 B8 Ω0(¹⁵N) + Ω1(¹³C′) + Ω2(¹³C^(α)) 122.043 ±0.167 B9 Ω0(¹⁵N) − Ω1(¹³C′) + Ω2(¹³C^(α)) 117.721 ± 0.167 B10 Ω0(¹⁵N) +Ω1(¹³C′) − Ω2(¹³C^(α)) 111.432 ± 0.167 B11 Ω0(¹⁵N) − Ω1(¹³C′) −Ω2(¹³C^(α)) 107.122 ± 0.167 B12 Ω0(¹⁵N) + Ω1(¹³C′) 116.832 ± 0.106 B13Ω0(¹⁵N) − Ω1(¹³C′) 112.351 ± 0.106 B14 Ω0(¹⁵N) 114.577 ± 0.078 B15Single-quantum shifts [ppm] Ω0(¹⁵N) 114.593 ± 0.040 Ω1(¹³C′) 175.133 ±0.017 Ω2(¹³C^(α))  58.427 ± 0.019 Ω3(¹H^(α))  3.347 ± 0.006 (B) (5,2)DHACACONHN Linear combinations of shifts [Ω₀(¹⁵N) of Ser 65 and of Glu 64otherwise] measured along ω₁ [ppm] Ω₀(¹⁵N) + Ω₁(¹³C′) + Ω₂(¹³C^(α)) +Ω₃(¹H^(α)) 108.510 ± 0.167 B1 Ω₀(¹⁵N) − Ω₁(¹³C′) + Ω₂(¹³C^(α)) +Ω₃(¹H^(α)) 103.758 ± 0.167 B2 Ω₀(¹⁵N) + Ω₁(¹³C′) − Ω₂(¹³C^(α)) +Ω₃(¹H^(α))  97.642 ± 0.167 B3 Ω₀(¹⁵N) − Ω₁(¹³C′) − Ω₂(¹³C^(α)) +Ω₃(¹H^(α))  92.982 ± 0.167 B4 Ω₀(¹⁵N) + Ω₁(¹³C′) + Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 136.891 ± 0.167 B5 Ω₀(¹⁵N) − Ω₁(¹³C′) + Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 131.088 ± 0.167 B6 Ω₀(¹⁵N) + Ω₁(¹³C′) − Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 125.054 ± 0.167 B7 Ω₀(¹⁵N) − Ω₁(¹³C′) − Ω₂(¹³C^(α)) −Ω₃(¹H^(α)) 121.270 ± 0.167 B8 Ω₀(¹⁵N) + Ω₁(¹³C′) + Ω₂(¹³C^(α)) 122.727 ±0.167 B9 Ω₀(¹⁵N) + Ω₁(¹³C′) − Ω₂(¹³C^(α)) 111.894 ± 0.167 B10 Ω₀(¹⁵N) −Ω₁(¹³C′) + Ω₂(¹³C^(α)) 117.984 ± 0.167 B11 Ω₀(¹⁵N) − Ω₁(¹³C′) −Ω₂(¹³C^(α)) 107.206 ± 0.167 B12 Ω₀(¹⁵N) + Ω₁(¹³C′) 116.198 ± 0.106 B13Ω₀(¹⁵N) − Ω₁(¹³C′) 112.608 ± 0.106 B14 Ω₀(¹⁵N) 114.886 ± 0.078 B15Single-quantum shifts [ppm] Ω₀(¹⁵N) (Ser 65) 114.913 ± 0.040 Ω₁(¹³C′)175.210 ± 0.017 −0.077 Ω₂(¹³C^(α))  58.440 ± 0.019 −0.013 Ω₃(¹H^(α)) 3.344 ± 0.006 +0.003

[0253] TABLE 4 Chemical Shifts Measured in (5,3)D HACA,CONHN/(5,3)DHACACO NHN Recorded for TT212 (see FIG. 22). The Underlined Valuesin the Lower Right Represent the Differences of Single-Quantum ShiftsObtained from (5,3)D HACA,CO NHN and (5,3)D HACACONHN. (A) (5,3)DHACA,CONHN Linear combinations of shifts (Ile 25) measured along ω₁[ppm] Ω₀(¹³C′) + Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) 180.354 ± 0.067 B1 Ω₀(¹³C′) −Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) 167.916 ± 0.067 B2 Ω₀(¹³C′) + Ω₁(¹³C^(α)) −Ω₂(¹H^(α))) 185.688 ± 0.067 B3 Ω₀(¹³C′) − Ω₁(¹³C^(α)) − Ω₂(¹H^(α))173.824 ± 0.067 B4 Ω₀(¹³C′) + Ω₁(¹³C^(α)) 183.169 ± 0.067 B5 Ω₀(¹³C′) −Ω₁(¹³C^(α)) 170.699 ± 0.067 B6 Ω₀(¹³C′) 177.140 ± 0.045 B7Single-quantum shifts [ppm] Ω₀(¹³C′) 176.970 ± 0.024 Ω₁(¹³C^(α))  62.389± 0.027 Ω₂(¹H^(α))  4.073 ± 0.009 (B) (5,3)D HACACONHN Linearcombinations of shifts (Ile 25) measured along ω₁ [ppm] Ω₀(¹³C′) +Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) 180.223 ± 0.067 B1 Ω₀(¹³C′) − Ω₁(¹³C^(α)) +Ω₂(¹H^(α)) 168.256 ± 0.067 B2 Ω₀(¹³C′) + Ω₁(¹³C^(α)) − Ω₂(¹H^(α)))185.907 ± 0.067 B3 Ω₀(¹³C′) − Ω₁(¹³C^(α)) − Ω₂(¹H^(α)) 173.603 ± 0.067B4 Ω₀(¹³C′) + Ω₁(¹³C^(α)) 183.052 ± 0.067 B5 Ω₀(¹³C′) − Ω₁(¹³C^(α))170.933 ± 0.067 B6 Ω₀(¹³C′) 177.075 ± 0.045 B7 Single-quantum shifts[ppm] Ω₀(¹³C′) 177.007 ± 0.024 −0.037 Ω₁(¹³C^(α))  62.325 ± 0.027 +0.064Ω₂(¹H^(α))  4.087 ± 0.009 −0.014

[0254] TABLE 5 Chemical Shifts Measured in (4,3)D CB,CACONHN/(4,3)DCBCACO NHN Recorded for Ubiquitin (see FIG. 23). The UnderlinedValues in the Lower Right Represent the Differences of Single-QuantumShifts Obtained from (4,3)D CB,CACONHN and (4,3)D CBCACONHN. (A) (4,3)DCBCA,CO NHN Linear combinations of shifts (Ser 65) measured along ω₁[ppm] Ω₀(¹³C′) + Ω₁(¹³C^(α)) 191.359 ± 0.067 B1 Ω₀(¹³C′) + Ω₁(¹³C^(β))195.451 ± 0.067 B1 Ω₀(¹³C′) − Ω₁(¹³C^(α)) 152.401 ± 0.067 B2 Ω₀(¹³C′) −Ω₁(¹³C^(β)) 148.249 ± 0.067 B2 Ω₀(¹³C′) 171.848 ± 0.045 B3Single-quantum shifts [ppm] Ω₀(¹³C′) 171.862 ± 0.027 Ω₁(¹³C^(α))  60.789± 0.047 Ω₁(¹³C^(β))  64.911 ± 0.047 (B) (4,3)D CBCACONHN Linearcombinations of shifts (Ser 65) measured along ω₁ [ppm] Ω₀(¹³C′) +Ω₁(¹³C^(α)) 191.533 ± 0.067 B1 Ω₀(¹³C′) + Ω₁(¹³C^(β)) 195.530 ± 0.067 B1Ω₀(¹³C′) − Ω₁(¹³C^(α)) 152.267 ± 0.067 B2 Ω₀(¹³C′) − Ω₁(¹³C^(β)) 148.225± 0.067 B2 Ω₀(¹³C′) 171.887 ± 0.045 B3 Single-quantum shifts [ppm]Ω₀(¹³C′) 171.888 ± 0.027 −0.026 Ω₁(¹³C^(α))  60.943 ± 0.047 −0.154Ω₁(¹³C^(β))  64.962 ± 0.047 −0.051

[0255] TABLE 6 Chemical Shifts Measured in (5,3)D HACA,CONHN/(5,3)DHACACO NHN Recorded for Ubiquitin (see FIG. 24). The UnderlinedNumbers in the Lower Right Represent the Differences of Single-QuantumShifts Obtained from (5,3)D HACA,CONHN and (5,3)D HACACONHN. (A) (5,3)DHACA,CONHN Linear combinations of shifts (Ser 65) measured along ω₁[ppm] (FIG. 21) Ω₀(¹³C′) + Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) 176.020 ± 0.067 B1Ω₀(¹³C′) − Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) 166.513 ± 0.067 B2 Ω₀(¹³C′) +Ω₁(¹³C^(α)) − Ω₂(¹H^(α)) 177.233 ± 0.067 B3 Ω₀(¹³C′) − Ω₁(¹³C^(α)) −Ω₂(¹H^(α)) 167.684 ± 0.067 B4 Ω₀(¹³C′) + Ω₁(¹³C^(α)) 176.656 ± 0.067 B5Ω₀(¹³C′) − Ω₁(¹³C^(α)) 167.090 ± 0.067 B6 Ω₀(¹³C′) 171.848 ± 0.045 B7Single-quantum shifts [ppm] Ω₀(¹³C′) 171.863 ± 0.024 Ω₁(¹³C^(α))  61.030± 0.027 Ω₂(¹H^(α))  4.630 ± 0.009 (B) (5,3)D HACACONHN [ubiquitin]Linear combinations of shifts (Ser 65) measured along ω₁ [ppm] (FIG. 21)Ω₀(¹³C′) + Ω₁(¹³C^(α)) + Ω₂(¹H^(α)) 175.975 ± 0.067 B1 Ω₀(¹³C′) +Ω₁(¹³C^(α)) − Ω₂(¹H^(α))) 177.140 ± 0.067 B2 Ω₀(¹³C′) − Ω₁(¹³C^(α)) −Ω₂(¹H^(α)) 167.770 ± 0.067 B3 Ω₀(¹³C′) − Ω₁(¹³C^(α)) + Ω₂(¹H^(α))166.610 ± 0.067 B4 Ω₀(¹³C′) + Ω₁(¹³C^(α)) 176.598 ± 0.067 B5 Ω₀(¹³C′) −Ω₁(¹³C^(α)) 167.197 ± 0.067 B6 Ω₀(¹³C′) 171.887 ± 0.045 B7Single-quantum shifts [ppm] Ω₀(¹³C′) 171.882 ± 0.024 −0.019 Ω₁(¹³C^(α)) 60.949 ± 0.027 +0.081 Ω₂(¹H^(α))  4.634 ± 0.009 −0.004

[0256] Automated resonance assignment (Szyperski et al., J. Biomol. NMR11:387-405 (1998); Moseley et al., Meth. Enzymol. 339:91-108 (2002),which are hereby incorporated by reference in their entirety), forhigh-throughput structure determination in structural genomics(Montelione et al., Nature Struc. Biol. 7:982-984 (2000), which ishereby incorporated by reference in its entirety) may profit fromemployment of GFT NMR in either of the two ways described in thefollowing. First, peak lists of GFT NMR spectra may be used directly toestablish sequential connectivities. Then, the extended set ofconnectivities (see FIGS. 21-23) corresponding to the matching of2^(m)−1 “linear combinations” of shifts is redundant and contains NDinformation. Notably, automated resonance assignment protocols arerather sensitive to the lack of even a smaller number of sequentialconnectivities. Hence, one can expect to establish more reliablestrategies when compared to the use of conventional spectroscopy, alsofor smaller proteins with molecular weights around 10 kDa.Alternatively, the GFT NMR peak lists can be used to calculate ND peaklists containing precise single-quantum shifts. Subsequently, sequentialconnectivities are established based on matching of single-quantumshifts. Due to the increased accuracy of the GFT shift measurements,correspondingly reduced matching tolerances (defined as the chemicalshift difference between two shift values below which these areconsidered to be identical) can be employed. For example, the programAUTOASSIGN (Monleon et al., J. Struc. Func. Genomics 2:93-101 (2002),which is hereby incorporated by reference in its entirety) is routinelyexecuted with matching tolerances of 0.4 ppm for ¹³C^(α/β) shifts, 0.25ppm for ¹³C′ shifts and 0.04 ppm for ¹H^(α) shifts measured in indirectdimensions of FT triple resonance NMR spectra. Setting the matchingtolerance for analysis of (5,2)D and (5,3)D GFT NMR derived ND peak listto about 2 times the maximal shift difference (Tables 3 to 5), oneobtains as a first estimate: ˜0.15 ppm for ¹³C^(α) shifts, ˜0.15 ppm for¹³C′ shifts and ˜0.02 ppm for ¹H^(α) shifts. Future statistical analysisof several GFT NMR spectra and the use of AUTOASSIGN for GFT NMR datahave to reveal the magnitude of the reduction of matching tolerancesmore accurately, but the estimates presented herein clearly show that asignificant reduction can be anticipated. Notably, the accuracy of shiftmeasurements using constant time GFT NMR experiments is independent oftransverse relaxation rates (which solely determine the peak intensity)and thus independent of the molecular weight.

[0257] In principle, with respect to the detection of sequential peaksin the experiments providing the intraresidue connectivities, one may“filter out” the sequential connectivities (e.g., Brutscher, J. Magn.Reson. 156:155-159 (2002), which is hereby incorporated by reference inits entirety). However, for some applications, it is preferable not toeliminate sequential peaks, since (i) such filtering compromises on thesensitivity, (ii) the sequential peaks can be readily identified in thesequential congener, and (iii) the sequential peaks in the intraresidueexperiment can be used to accurately adjust the calibration of the twoGFT NMR spectra used in conjunction. For automated assignment protocols,the procedure of point (iii) is of outstanding value to reduce matchingtolerances and is thus routinely employed. At highest magnetic fields(900° MHz ¹H resonance frequency), it might be advantageous to designGFT experiments providing the sequential connectivities in a mannersuggested by Meissner et al., J. Magn. Reson. 150:100-104 (2001), whichis hereby incorporated by reference in its entirety.

[0258] In view of the introduction of cryogenic probes, which reduce NMRmeasurement times by a factor of 10 or more (Monleon et al., J. Struc.Func. Genomics 2:93-101 (2002), which is hereby incorporated byreference in its entirety), GFT NMR experiments providing 4D and 5D NMRspectral information are highly attractive also for larger systems. Forexample, (5,2)D HACACONHN/HACA,CONHN and (4,3)D CBCACONHN/CBCA,CONENwere acquired in only 10.6 and 11.2 hours, respectively, for an 8.6 kDaprotein and it can thus be expected that similarly short measurementtimes are feasible for medium-sized protein up to about 20 kDa whenusing cryogenic probes. In fact, the (5,3)D data sets of 14 kDa TT212(FIG. 22) were acquired in about 60 hours, so that the same data couldhave been recorded within a few hours with a cryogenic probe. Apart fromsensitivity, spectral resolution is critical for employment ofmultidimensional NMR. At high magnetic fields, (4,3)D and (5,3)D¹⁵N-resolved GFT NMR experiments are well suited to approach largeproteins, at least to the extent such conventional ¹⁵N-resolved 3Dspectra are currently used. For the (5,2)D experiments, one needs toconsider that peak dispersion increases linearly from third order (2D[¹⁵N, ¹H]-HSQC), to second order to first order and to basic spectra(see FIG. 17). Moreover, future research needs to show how effectivelycomputer supported “bottom-up” identification of chemical shiftmultiplets restores the 5D dispersion. Certainly, the dispersion of the2D [¹⁵N, ¹H]-HSQC provides a good initial indication with respect to thedegree of overlap that needs to be resolved during the “bottom-up”assignment. At 90° MHz ¹H resonance frequency, 20-25 kDa proteins oftenexhibit rather well resolved 2D [¹⁵N, ¹H]-TROSY (Pervushin et al., Proc.Natl. Acad. Sci. USA 99:8009-8014 (1997), which is hereby incorporatedby reference in its entirety) spectra, and thus it is expected thatproteins up to a least 20 kDa might well be approached using (5,2)DGFT-TROSY NMR at such highest field strengths.

[0259] Finally, future research will show to which extent theacquisition speed of GFT NMR can be further increase (Frydman et al.,Proc. Natl. Acad. Sci. USA 99:15858-15862 (2002), which is herebyincorporated by reference in its entirety), or Hadamard-type samplingschemes (Kupce et al., J. Magn. Reson. Ser. A 105 310-315 (1993); Kupceet al., J. Biomol. NMR 25:349-354 (2003), which are hereby incorporatedby reference in their entirety). Moreover, it is conceivable that the“sampling demand” of GFT NMR can be further reduced by (i) non-linearsampling (Schmieder et al., J. Biomol. NMR 4:483-490° (1994), which ishereby incorporated by reference in its entirety), (ii) the employmentof the filter diagonalization approach for data processing (Wall et al.,J. Chem. Phys. 112:8011-8022 (1995); Hu et al., J. Magn. Reson.134:76-87 (1998), which are hereby incorporated by reference in theirentirety), or (iii) the use of “three-way decomposition” (Gutmanas etal., J. Biomol. NMR 24:191-201 (2002), which is hereby incorporated byreference in its entirety).

EXAMPLE 11 Implementation and Analyses of the (4,3)D HNNCACBCA, (4,3)DHNN(CO)CACBCA/(4,3)D CBCACA(CO)NHN, (5,3)D HBHACBCACA(CO)NHN, (5,3)D HCCCH—COSY, (5,3)D HBCBCGCDHD, and (4,2)D HCCH—COSY GFT NMR Experiments

[0260] The following GFT NMR experiments were conducted for theassignment of polypeptide backbone and sidechain resonances: (i) (4,3)DHNNCACBCA GFT NMR experiment (FIG. 5A), (ii) (4,3)D CBCACA(CO)NHN/(4,3)DHNN(CO)CACBCA GFT NMR experiments (FIG. 5B), (iii) (5,3)DHBHACBCACA(CO)NHN GFT NMR experiment (FIG. 5C), (iv) (5,3)D HCC,CH—COSYGFT NMR experiment (FIG. 5D), (v) (5,3)D HBCBCGCDHD GFT NMR experiment(FIG. 5E), (vi) (4,2)D HCCH—COSY GFT NMR experiment (FIG. 5F), and (vii)(5,2)D HCCCH—COSY GFT NMR experiment (FIG. 5G).

[0261] In the (4,3)D HNNCACBCA GFT NMR experiment, after independentfrequency labeling of ¹³C^(α) and ¹³C^(β) spins of both amino acidresidues i and i−1 (hereinafter referred to as i/i−1), magnetization istransferred to the respective ¹³C^(α) _(i/i−1) spin, which is thenfrequency labeled and detected in quadrature in each of the 3D spectraconstituting the (4,3)D experiment. Thus, for a given ¹⁵N_(i) and ¹H^(N)_(i)chemical shift, the 2 basic spectra comprise peaks at Ω₀(¹³C^(α)_(i))±Ω₁(¹³C^(α/β) _(i)) and Ω₀(¹³C^(α) _(i−1))±Ω₁ (¹³C^(α/β) _(i−1)).The first order central peak spectrum for (4,3)D HNNCACBCA was acquiredusing a 3D HNNCA pulse sequence comprising peaks at Ω₀(¹³C^(α) _(i)) andΩ₀(¹³C^(α) _(i−1)).

[0262] In the (4,3)D HNN(CO)CACBCA/(4,3)D CBCACA(CO)NHN GFT NMRexperiments, the same principle as described in the (4,3)D HNNCACBCA GFTNMR experiment was used, except that the 2 basic spectra comprise, for agiven ¹⁵N_(i) and ¹H^(N) _(i)chemical shift, peaks from only amino acidresidue i−1 at Ω₀(¹³C^(α) _(i−1)) ±Ω₁(¹³C^(α/β) _(i−1)) chemical shifts.(4,3)D HNN(CO)CACBCA GFT NMR experiment is an “out-and-back” type ofexperiment, while (4,3)D CBCACA(CO)NHN GFT NMR experiment is an“out-and-stay” type. The first order central peak spectrum for (4,3)DHNN(CO)CACBCA/(4,3)D CBCACA(CO)NHN GFT NMR experiments comprising peaksat Ω₀(¹³C^(α) _(i−1)) was acquired using a 3D HNN(CO)CA pulse sequence.

[0263] Using the above-described (4,3)D HNNCACBCA GFT NMR experiment andthe (4,3)D HNN(CO)CACBCA/(4,3)D CBCACA(CO)NHN GFT NMR experiments in acombined fashion, one can sequentially assign residue pairs (i/i−1) in apolypeptide chain, as illustrated in FIG. 25 for Glu 73 of the 17 kDaprotein ER75. FIG. 26 illustrates the sequential walk for residues Val27 to Ile 30 of the 7 kDa protein GR2 using the (4,3)D HNNCACBCA GFT NMRexperiment and the (4,3)D HNN(CO)CACBCA/(4,3)D CBCACA(CO)NHN GFT NMRexperiments.

[0264] Having obtained the chemical shifts of ¹³C^(α/β) spins for agiven amino acid residue, the (5,3)D HBHACBCACA(CO)NHN GFT NMRexperiment can be used to obtain ¹H^(α/β) chemical shifts. In thisexperiment, frequency labeling of the ¹H^(α/β) spin was carried outsimultaneously with that of ¹³C^(α/β) spins. Thus, for a given ¹⁵N_(i)and ¹H^(N) _(i)chemical shift, the 4 basic spectra comprise peaks atΩ₀(¹³C^(α) _(i−1))±Ω₁(¹³C^(α) _(i−1))±Ω₂(¹H^(α) _(i−1)) and Ω₀(¹³C^(α)_(i−1))±Ω₁(¹³C^(β) _(i−1))±Ω₂(¹H^(β) _(i−1)). The ¹³C^(α/β) steady-statemagnetization was used to obtain the two first order central peakspectra comprising peaks at Ω₀(¹³C^(α) _(i−1))±Ω₁(¹³C^(α/β) _(i−1)). Thesecond order central peak spectrum was acquired using a 3D HNN(CO)CApulse sequence comprising peaks at Ω₀(¹³C^(α) _(i−1)). FIG. 27illustrates peak patterns observed in the (5,3)D HBHACBCACA(CO)NHN GFTNMR spectra, as well as the identity in the peak patterns observed inthe basic spectra of the (4,3)D CBCACA(CO)NHN GFT NMR experiment and thefirst order central peak spectra of the (5,3)D HBHACBCACA(CO)NHN GFT NMRexperiment.

[0265] The information of ¹H^(α/β) and ¹³C^(α/β) chemical shifts can beused to assign the more peripheral spins of the aliphatic sidechain of agiven amino acid residue by employing the (5,3)D HCC, CH—COSY GFT NMRexperiment. For a given ¹³C_(i) and ¹H_(i) chemical shift, the 4 basicspectra comprise peaks at Ω₀(¹³C_(i))±Ω₁(¹³C_(i))±Ω₂(¹H_(i)) andΩ₀(¹³C_(i))±Ω₁(¹³C^(coupled) _(i))±Ω₂(¹H^(coupled) _(i)). The peakpattern observed in the (5,3)D HCC, CH—COSY GFT NMR experiment isillustrated in FIG. 28. ¹³C steady-state magnetization was used toobtain the two first order central peak spectra comprising peaks atΩ₀(¹³C_(i))±Ω₁(¹³C_(i)) and Ω₀(¹³C_(i))±Ω₁(¹³C_(i) ^(coupled)). Thesecond order central peak spectrum was acquired using a 3D (H)C,CH—COSYpulse sequence and comprises peaks at Ω₀(¹³C_(i)). The same pulse schemeas used for the (5,3)D HCC, CH—COSY GFT NMR experiment can also be usedfor assigning aromatic sidechain resonances in proteins by tuning theconstant time delay to a value suited for transferring magnetizationbetween aromatic ¹³C-spins.

[0266] Resonance assignments of aromatic sidechain spins can be achievedby using a (5,3)D HBCBCGCDHD GFT NMR experiment and (4,2)D HCCH—COSY GFTNMR experiment. In the (5,3)D HBCBCGCDHD GFT NMR experiment, for a given¹³C^(δ) and ¹H^(δ) chemical shift, the 4 basic spectra comprise peaks atΩ₀(¹³C^(δ))±Ω₁(¹³C^(β))±Ω₂(¹H^(β)). In the (^(4,2))D HCCH—COSY GFT NMRexperiment, for a given ¹H_(i) chemical shift, the 4 basic spectracomprise peaks at Ω₀(¹³C_(i))±Ω₁(¹³C_(i))±Ω₂(¹H_(i)) andΩ₀(¹³C_(i))±Ω₂(¹³C^(coupled) _(i))±Ω₂(¹H_(i) ^(coupled)). The peakpatterns observed in these spectra are illustrated in FIG. 29 and 30,respectively, for the 8.6 kDa protein ubiquitin. The ¹³C steady-statemagnetization was used to obtain the two first order central peakspectra comprising peaks for the (5,3)D HBCBCGCDHD GFT NMR experiment atΩ₀(¹³C^(δ))±Ω₁(¹³C^(β)) and for the (4,2)D HCCH—COSY GFT NMR experimentat Ω₀(¹³C_(i))±Ω₁(¹³C_(i)) and Ω₀(¹³C_(i))±Ω₁(¹³C_(i) ^(coupled)). Inthe (5,3)D HBCBCGCDHD experiment, the chemical shift of the ¹³C^(δ) spinof aromatic amino acid residues was detected in quadrature along the ω₁dimension in all the 3D spectra constituting the (5,3)D experiment. Thesecond order central peak spectra for the (4,2)D HCCH—COSY and (5,3)DHBCBCGCDHD were acquired using the pulse sequence for a 2D [¹³C-¹H] HSQC(comprising peaks at Ω₀(¹³C_(i))) and 3D (HBCB)CGCDHD—COSY (comprisingpeaks at Ω₀(¹³C^(δ))), respectively. The same pulse scheme as used forthe (4,2)D HCCH—COSY experiment can also be used for assigning aliphaticside-chain resonances in proteins by tuning the constant time delay to avalue suited for transferring magnetization between aliphatic ¹³C-spins.

[0267] The assignment of the side-chain chemical shifts can be furthersupported with the (5,2)D HCCCH—COSY experiment. In this experiment, fora ¹³C_(i) and a ¹H_(i) chemical shift, the 8 basic spectra comprisepeaks at: Ω₀(¹³C_(i))±Ω₁(¹³C_(i))±Ω₂(¹³C_(i))±Ω₃(¹H_(i)),Ω₀(¹³C_(i))±Ω₁(¹³C_(i))±Ω₂(¹³C_(i) ^(coupled))±Ω₃(¹H_(i) ^(coupled)),and Ω₀(¹³C_(i))±Ω₁(¹³C_(i) ^(coupled))±Ω₂(¹³C_(i)^(coupled-2))±Ω₃(¹H_(i) ^(coupled-2)). ¹³C steady-state magnetizationcan be used to obtain the 4 first order central peak spectra comprisingpeaks at: Ω₀(¹³C_(i))±Ω₁(¹³C_(i))±Ω₂(¹³C_(i)),Ω₀(¹³C_(i))±Ω₁(¹³C_(i))±Ω₂(¹³C_(i) ^(coupled)), andΩ₀(¹³C_(i))±Ω₁(¹³C_(i) ^(coupled))±Ω₂(¹³C_(i) ^(coupled-2)). The firstorder central peak spectra of HCCH—COSY represent the second ordercentral peak spectra for the (5,2)D HCCCH—COSY experiment, comprisingpeaks at: Ω₀(¹³C_(i))±Ω₁(¹³C_(i)) and Ω₀(¹³C_(i))±Ω₁(¹³C_(i)^(coupled)). The third order central peak spectrum is acquired using a2D [¹³C-¹H] HSQC pulse sequence comprising peaks at Ω₀(¹³C_(i)).

[0268] The radio frequency pulse schemes for the experiments describedin this example are shown in FIGS. 9-15. Tables 7-9 list the experimentsand all the relevant experimental parameters used in implementation forthe proteins GR2, ubiquitin and ER75. TABLE 7 Acquisition Parameters forGFT NMR Experiments Recorded for the 7 kDa Protein GR2. (5,3)D (4,3)D(4,3)D (5,3)D HCC,CH- HNNCACBCA CBCACA(CO)NHN HBHACBCACA(CO)NHN COSY ¹HResonance 600 MHz 600 MHz 600 MHz 600 MHz Frequency No. of Points^(a)(t₁, t₂, t₃) Collected: 64, 24 512 64, 24 512 64, 24 512 100, 22, 512After LP: 64, 24, 512 64, 24 512 64, 24 512 100, 22, 512 After Zero 256,64, 1024 256, 64, 1024 256, 64, 1024 256, 64, 1024 Filling Window sine90/90/70 sine 90/90/70 sine 90/90/70 sine 90/90/70 Functions^(b) No. ofTransients^(c) 2 2 2 2 Spectral Width^(d) 12000, 1600, 12000, 1600, 600025000, 1600, 6000 25000, 4500, (ω₁, ω₂, ω₃; Hz) 6000 6000 t_(max) ^(e)(ms) 5.3, 15.0, 85.2 5.3, 15.0, 85.2 2.7, 15.0, 85.2 5.0, 4.0, 85.2Carrier Position^(f) 43.0, 120.4, 43.0, 120.4, 4.78−1.0(¹H)/43.0(¹³C)/56.3 0.0(¹H)/ (ω₁, ω₂, ω₃; ppm) 4.78 (¹³C), 120.4,4.78 43.0(¹³C), 43.0, 4.78 Recycle Delay^(g) 0.7 0.7 1.0 0.7 (s)Collection Time 6.5 6.5 32 22 (hrs)^(h)

[0269] TABLE 8 Acquisition Parameters for GFT NMR Experiments Recordedfor the 17 kDa Protein ER75. (4, 3) D (4, 3) D (5,3) D HNNCACBCAHNN(CO)CACBCA HCC,CH-COSY Spectrometer 750 MHz 750 MHz 750 MHz No. ofPoints^(a) (t₁, t₂, t₃) Collected: 64, 32, 512 64, 32, 512 100, 24, 512After LP: 64, 32, 512 64, 32, 512 100, 24, 512 After Zero 256, 64, 1024256, 64, 1024 256, 64, 1024 Filling Window sine 90/90/70 sine 90/90/70sine 90/90/70 Functions^(b) No. of 8 8 4 Transients^(c) Spectral 14000,2200, 14000, 2200, 9000 30000, 5400, Width^(d) 9000 9000 (ω₁, ω₂, ω₃;Hz) t_(max) (ms)^(e) 4.6, 14.1, 56.8 4.6, 14.1, 56.8 3.3, 4.4, 56.8Carrier 42.5, 117.2, 42.5, 117.2, 4.78 0.0 (¹H)/ Position^(f) 4.78 42.5(¹³C), (ω₁, ω₂, ω₃; 42.5, 4.78 ppm) 4.78 Recycly Delay^(g) 1.0 1.0 1.0(s) Collection 42 42 96 Time (hrs)^(h)

[0270] TABLE 9 Acquisition Parameters for GFT NMR Experiments Recordedfor the 8.6 kDa Protein Ubiquitin (4, 2) D (5, 3) D HCCH-COSY HBCBCGCDHDSpectrometer 600 MHz 600 MHz No. of Points^(a) (t₁, t₂, t₃) Collected:64, 1024 30, 10, 512 After LP: 64, 1024 30, 10, 512 After Zero Filling256, 1024 256, 32, 1024 Window Functions^(b) sine 90/70 sine 90/90/70No. of Transients^(c) 4 4 Spectral Width^(d) 14000, 6794 8000, 2500,6794 (ω₁, ω₂, ω₃; HZ) t_(max) (ms) 4.5, 150.5 3.75, 4.0, 150.5 e CarrierPosition^(f) 4.78 (¹H)/125 (¹³C), 4.78 (¹H)/38.0 (ω₁, ω₂, ω₃; ppm) 4.78(¹³ C)/125.0(¹³ C), 135.0, 4.78 Recycle Delay (s)^(g) 1.0 1.0 CollectionTime (hrs)^(h) 2.5 12

[0271] Although preferred embodiments have been depicted and describedin detail herein, it will be apparent to those skilled in the relevantart that various modifications, additions, substitutions, and the likecan be made without departing from the spirit of the invention and theseare therefore considered to be within the scope of the invention asdefined in the claims which follow.

What is claimed:
 1. A method of conducting a (N,N−K) dimensional (D)G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment, wherein N is the dimensionality of an N-dimensional (ND)Fourier transformation (FT) NMR experiment and K is the desiredreduction in dimensionality relative to N, said method comprising:providing a sample; applying radio frequency pulses for the ND FT NMRexperiment to the sample; selecting m indirect chemical shift evolutionperiods of the ND FT NMR experiment, wherein m equals K+1; jointlysampling the m indirect chemical shift evolution periods; independentlycosine and sine modulating NMR signals detected in a direct dimension togenerate (N−K)D basic NMR spectra comprising frequency domain signalswith 2^(K) chemical shift multiplet components, thereby enablingphase-sensitive sampling of all jointly sampled m indirect chemicalshift evolution periods; and transforming the (N−K) D basic NMR spectrainto (N−K) D phase-sensitively edited basic NMR spectra, wherein the2^(K) chemical shift multiplet components of the (N−K) D basic NMRspectra are edited to yield (N−K) D phase-sensitively edited basic NMRspectra having individual chemical shift multiplet components.
 2. Themethod according to claim 1, wherein said transforming is carried out byapplying a G-matrix defined as${{\hat{G}(K)} = \left\lbrack {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i\end{bmatrix}} \right\rbrack},$

wherein i={square root}{square root over (−1)}, under conditionseffective to edit the chemical shift multiplet components in a timedomain.
 3. The method according to claim 1, wherein said transforming iscarried out by applying a F-matrix defined as {circumflex over(F)}(K)={circumflex over (F)}(K−1) {circle over (x)}{circumflex over(F)}(1), wherein ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$

under conditions effective to edit the chemical shift multipletcomponents in a frequency domain.
 4. The method according to claim 1further comprising: selecting m′ indirect chemical shift evolutionperiods of the (N−K)D FT NMR experiment, wherein m′ equals K′+1; jointlysampling the m′ indirect chemical shift evolution periods; independentlycosine and sine modulating NMR signals detected in a direct dimension togenerate (N−K−K′)D basic NMR spectra comprising frequency domain signalswith 2^(K′) chemical shift multiplet components, thereby enablingphase-sensitive sampling of all jointly sampled m′ indirect chemicalshift evolution periods; and transforming the (N−K−K′) D basic NMRspectra into (N−K−K′) D phase-sensitively edited basic NMR spectra,wherein the 2^(K′) chemical shift multiplet components of the (N−K−K′) Dbasic NMR spectra are edited to yield (N−K−K′) D phase-sensitivelyedited basic NMR spectra having individual chemical shift multipletcomponents.
 5. The method according to claim 4 further comprising:repeating one or more times said selecting, said jointly sampling, saidindependently cosine and sine modulating, and said transforming, whereinm′ is modified for each repetition.
 6. The method according to claim 1further comprising: repeating one or more times said selecting, saidjointly sampling, said independently cosine and sine modulating, andsaid transforming, wherein, for each repetition, said selectingcomprises selecting m-j indirect chemical shift evolution periods out ofthe m indirect chemical shift evolution periods, wherein j ranges from 1to K, under conditions effective to generate 2^(K-j)jth order centralpeak NMR spectra.
 7. The method according to claim 1, wherein saidapplying radiofrequency pulses is carried out by applying radiofrequencypulses of N-dimensional nuclear Overhauser enhancement spectroscopy(NOESY).
 8. The method according to claim 1, wherein said applyingradiofrequency pulses is carried out by applying radiofrequency pulsesof N-dimensional transverse relaxation optimized spectroscopy (TROSY).9. The method according to claim 1, wherein said applying radiofrequencypulses is carried out so that spin-spin couplings are measured.
 10. Themethod according to claim 9, wherein said spin-spin couplings areresidual dipolar spin-spin coupling constants.
 11. The method accordingto claim 1, wherein said jointly sampling the m indirect chemical shiftevolution periods is achieved with a single continuous acquisition. 12.The method according to claim 1, wherein said applying radiofrequencypulses is carried out so that nuclear spin relaxation times are measuredby sampling nuclear spin relaxation delays.
 13. The method according toclaim 12 further comprising: jointly sampling said spin relaxationdelays with chemical shift evolution periods.
 14. The method accordingto claim 1, wherein N equals 5 and K equals 3 to conduct a (5,2)D[HACACONHN] GFT NMR experiment, wherein (a) said sample is a proteinmolecule having two consecutive amino acid residues, i−1 and i, and thechemical shift values for the following nuclei are measured: (1) anα-proton of amino acid residue i−1, ¹H^(α) _(i−1); (2) an α-carbon ofamino acid residue i−1, ¹³C^(α) _(i−1); (3) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (5) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i),(b) said selecting comprises selecting 4 chemical shift evolutionperiods of the 5D FT NMR experiment, ¹H^(α) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1), and ¹⁵N_(i), and (c) said jointly sampling comprises jointlysampling the 4 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1),¹⁵N_(i)).
 15. The method according to claim 14, wherein said applyingradiofrequency pulses comprises applying radio frequency pulses for a 5DFT NMR experiment according to the scheme shown in FIG.
 6. 16. Themethod according to claim 1, wherein N equals 5 and K equals 3 toconduct a (5,2)D [HACA,CONHN] GFT NMR experiment, wherein (a) saidsample is a protein molecule having an amino acid residue, i, and thechemical shift values for the following nuclei are measured: (1) anα-proton of amino acid residue i−1, ¹H^(α) _(i−1); (2) an α-carbon ofamino acid residue i−1, ¹³C^(α) _(i−1); (3) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) a polypeptidebackbone amide nitrogen of amino acid residue i−1, ¹⁵N_(i−1); and (5) apolypeptide backbone amide proton of amino acid residue i−1, ¹H^(N)_(i−1), (b) said selecting comprises selecting 4 chemical shiftevolution periods of the 5D FT NMR experiment, ¹H^(α) _(i−1), ¹³C^(α)_(i−1), ¹³C′_(i−1), and ¹⁵N_(i−1), and (c) said jointly samplingcomprises jointly sampling the 4 chemical shift evolution periods in anindirect time domain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α) _(i−1),¹³C_(i−1), ¹⁵N_(i−1)).
 17. The method according to claim 16, whereinsaid applying radiofrequency pulses comprises applying radiofrequencypulses for a 5D FT NMR experiment according to the scheme shown in FIG.7A.
 18. The method according to claim 1, wherein N equals 5 and K equals2 to conduct a (5,3)D [HACACONHN] GFT NMR experiment, wherein (a) saidsample is a protein molecule having two consecutive amino acid residues,i−1 and i, and the chemical shift values for the following nuclei aremeasured: (1) an α-proton of amino acid residue i−1, ¹H^(α) _(i−1); (2)an α-carbon of amino acid residue i−1, ¹³C^(α) _(i−1); (3) a polypeptidebackbone carbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (5) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) said selecting comprises selecting 3 chemical shiftevolution periods of the 5D FT NMR experiment, ¹H^(α) _(i−1), ¹³C^(α)_(i−1), and ¹³C′_(i−1), and (c) said jointly sampling comprises jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1)).
 19. Themethod according to claim 1, wherein N equals 5 and K equals 2 toconduct a (5,3)D [HACA,CONHN] GFT NMR experiment, wherein (a) saidsample is a protein molecule having an amino acid residue, i−1, and thechemical shift values for the following nuclei are measured: (1) anα-proton of amino acid residue i−1, ¹H^(α) _(i−1); (2) an α-carbon ofamino acid residue i−1, ¹³C^(α) _(i−1); (3) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) a polypeptidebackbone amide nitrogen of amino acid residue i−1, ¹⁵N_(i−1); and (5) apolypeptide backbone amide proton of amino acid residue i−1, ¹H^(N)_(i−1), (b) said selecting comprises selecting 3 chemical shiftevolution periods of the 5D FT NMR experiment, ¹H^(α) _(i−1), ¹³C^(α)_(i−1), and ¹³C′_(i−1), and (c) said jointly sampling comprises jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1)).
 20. Themethod according to claim 1, wherein N equals 4 and K equals 1 toconduct a (4,3)D [CBCACONHN] GFT NMR experiment, wherein (a) said sampleis a protein molecule having two consecutive amino acid residues, i−1and i, and the chemical shift values for the following nuclei aremeasured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i−1); (2) a polypeptide backbone carbonyl carbon of amino acid residuei−1, ¹³C′_(i−1); (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) said selecting comprises selecting 2chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^(α/β)_(i−1) and ¹³C′_(i−1), and (c) said jointly sampling comprises jointlysampling the 2 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C′_(i−1)).
 21. The methodaccording to claim 20, wherein said applying radio frequency pulsescomprises applying radio frequency pulses for a 4D FT NMR experimentaccording to the scheme shown in FIG.
 8. 22. The method according toclaim 1, wherein N equals 4 and K equals 1 to conduct a (4,3)D[CBCA,CONHN] GFT NMR experiment, wherein (a) said sample is a proteinmolecule having an amino acid residue, i−1, and the chemical shiftvalues for the following nuclei are measured: (1) α- and β-carbons ofamino acid residue i−1, ¹³C^(α/β) _(i−1); (2) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (3) a polypeptidebackbone amide nitrogen of amino acid residue i−1, ¹⁵N_(i−1); and (4) apolypeptide backbone amide proton of amino acid residue i−1, ¹H^(N)_(i−1), (b) said selecting comprises selecting 2 chemical shiftevolution periods of the 4D FT NMR experiment, ¹³C^(α/β) _(i−1) and¹³C′_(i−1), and (c) said jointly sampling comprises jointly sampling the2 chemical shift evolution periods in an indirect time domain dimension,t₁(¹³C^(α/β) _(i−1), ¹³C′_(i−1)).
 23. The method according to claim 22,wherein said applying radiofrequency pulses comprises applying radiofrequency pulses for a 4D FT NMR experiment according to the schemeshown in FIG. 7B.
 24. The method according to claim 1, wherein N equals4 and K equals 1 to conduct a (4,3)D [HNNCACBCA] GFT NMR experiment,wherein (a) said sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β-carbons of amino acidresidues i and i−1, ¹³C^(α/β) _(i/i−1); (2) a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); and (3) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i), (b) saidselecting comprises selecting 2 chemical shift evolution periods of the4D FT NMR experiment, ¹³C^(α/β) _(i/i−1) and ¹³C^(α) _(i/i−1), and (c)said jointly sampling comprises jointly sampling the 2 chemical shiftevolution periods in an indirect time domain dimension, t₁(¹³C^(α/β)_(i/i−1), ¹³C^(α) _(i/i−1)).
 25. The method according to claim 24,wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 4D FT NMR experiment according to the schemeshown in FIG.
 9. 26. The method according to claim 1, wherein N equals 4and K equals 2 to conduct a (4,2)D [HNNCACBCA] GFT NMR experiment,wherein (a) said sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β-carbons of amino acidresidues i and i−1, ¹³C^(α/β) _(i/i−1); (2) a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); and (3) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i), (b) saidselecting comprises selecting 3 chemical shift evolution periods of the4D FT NMR experiment, ¹³C^(α/β) _(i/i−1), ¹³C^(α) _(i/i−1), and ¹⁵N_(i),and (c) said jointly sampling comprises jointly sampling the 3 chemicalshift evolution periods in an indirect time domain dimension,t₁(¹³C^(α/β) _(i/i−1), ¹³C^(α) _(i/i−1), ¹⁵N_(i)).
 27. The methodaccording to claim 1, wherein N equals 4 and K equals 1 to conduct a(4,3)D [HNN(CO)CACBCA] GFT NMR experiment, wherein (a) said sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (3) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) said selecting comprises selecting 2 chemical shiftevolution periods of the 4D FT NMR experiment, ¹³C^(α/β) _(i−1) and¹³C^(α) _(i−1), and (c) said jointly sampling comprises jointly samplingthe 2 chemical shift evolution periods in an indirect time domaindimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1)).
 28. The methodaccording to claim 27, wherein said applying radiofrequency pulsescomprises applying radio frequency pulses for a 4D FT NMR experimentaccording to the scheme shown in FIG.
 10. 29. The method according toclaim 1, wherein N equals 4 and K equals 2 to conduct a (4,2)D[HNN(CO)CACBCA] GFT NMR experiment, wherein (a) said sample is a proteinmolecule having two consecutive amino acid residues, i−1 and i, and thechemical shift values for the following nuclei are measured: (1) α- andβ-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (3) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i),(b) said selecting comprises selecting 3 chemical shift evolutionperiods of the 4D FT NMR experiment, ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),and ¹⁵N_(i); and (c) said jointly sampling comprises jointly samplingthe 3 chemical shift evolution periods in an indirect time domaindimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹⁵N_(i)).
 30. The methodaccording to claim 1, wherein N equals 5 and K equals 2 to conduct a(5,3)D [HNNCOCACBCA] GFT NMR experiment, wherein (a) said sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1), (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) said selecting comprises selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1), (c) said jointly samplingcomprises jointly sampling the 3 chemical shift evolution periods in anindirect time domain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1)).
 31. The method according to claim 1, wherein N equals 5 andK equals 3 to conduct a (5,2)D [HNNCOCACBCA] GFT NMR experiment, wherein(a) said sample is a protein molecule having two consecutive amino acidresidues, i−1 and i, and the chemical shift values for the followingnuclei are measured: (1) α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1); (2) a polypeptide backbone carbonyl carbon of aminoacid residue i−1, ¹³C′⁻¹, (3) a polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i); and (4) a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i), (b) said selectingcomprises selecting 4 chemical shift evolution periods of the 5D FT NMRexperiment, ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i);and (c) said jointly sampling comprises jointly sampling the 4 chemicalshift evolution periods in an indirect time domain dimension,t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), ¹⁵N_(i)).
 32. Themethod according to claim 1, wherein N equals 4 and K equals 1 toconduct a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, wherein (a) saidsample is a protein molecule having two consecutive amino acid residues,i−1 and i, and the chemical shift values for the following nuclei aremeasured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i−1); (2) a polypeptide backbone amide nitrogen of amino acid residuei, ¹⁵N_(i); and (3) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) ^(i), (b) said selecting comprises selecting 2chemical shift evolution periods of the 4D FT NMR experiment, ¹³C^(α/β)_(i−1) and ¹³C^(α) _(i−1), and (c) said jointly sampling comprisesjointly sampling the 2 chemical shift evolution periods in an indirecttime domain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1)).
 33. Themethod according to claim 32, wherein said applying radio frequencypulses comprises applying radio frequency pulses for a 4D FT NMRexperiment according to the scheme shown in FIG.
 11. 34. The methodaccording to claim 1, wherein N equals 4 and K equals 2 to conduct a(4,2)D [CBCACA(CO)NHN] GFT NMR experiment, wherein (a) said sample is aprotein molecule having two consecutive amino acid residues, i−1 and i,and the chemical shift values for the following nuclei are measured: (1)(α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (3) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) said selecting comprises selecting 3 chemical shiftevolution periods of the 4D FT NMR experiment, ¹³C^(α/β) _(i−1), ¹³C^(α)_(i−1), and ¹⁵N_(i), and (c) said jointly sampling comprises jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹⁵N_(i)).
 35. Themethod according to claim 1, wherein N equals 5 and K equals 2 toconduct a (5,3)D [CBCACACONHN] GFT NMR experiment, wherein (a) saidsample is a protein molecule having two consecutive amino acid residues,i−1 and i, and the chemical shift values for the following nuclei aremeasured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i−1); (2) a polypeptide backbone carbonyl carbon of amino acid residuei−1, ¹³C′_(i−1), (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i), (b) said selecting comprises selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1), (c) said jointly samplingcomprises jointly sampling the 3 chemical shift evolution periods in anindirect time domain dimension, t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),¹³C′_(i−1)).
 36. The method according to claim 1, wherein N equals 5 andK equals 3 to conduct a (5,2)D [CBCACACONHN] GFT NMR experiment, wherein(a) said sample is a protein molecule having two consecutive amino acidresidues, i−1 and i, and the chemical shift values for the followingnuclei are measured: (1) (α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1); (2) a polypeptide backbone carbonyl carbon of aminoacid residue i−1, ¹³C′_(i−1), (3) a polypeptide backbone amide nitrogenof amino acid residue i, ¹⁵N_(i); and (4) a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i), (b) said selectingcomprises selecting 4 chemical shift evolution periods of the 5D FT NMRexperiment, ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i);(c) said jointly sampling comprises jointly sampling the 4 chemicalshift evolution periods in an indirect time domain dimension,t₁(¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), ¹⁵N_(i)).
 37. Themethod according to claim 1, wherein N equals 5 and K equals 2 toconduct a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment, wherein (a)said sample is a protein molecule having two amino acid residues, i andi−1, and the chemical shift values for the following nuclei aremeasured: (1) α- and β- protons of amino acid residue i−1, ¹H^(α/β)_(i−1); (2) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i−1); (3) a polypeptide backbone amide nitrogen of amino acid residuei, ¹⁵N_(i); and (4) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) _(i), (b) said selecting comprises selecting 3chemical shift evolution periods of the 5D FT NMR experiment, ¹H^(α/β)_(i−1), ¹³C^(α/β) _(i−1), and ¹³C^(α) _(i−1), and (c) said jointlysampling comprises jointly sampling the 3 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H^(α/β) _(i−1),¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1)).
 38. The method according to claim 37,wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 12. 39. The method according to claim 1, wherein N equals6 and K equals 3 to conduct a (6,3)D [HBHACBCACACONHN] GFT NMRexperiment, wherein (a) said sample is a protein molecule having twoamino acid residues, i and i−1, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β protons of amino acidresidue i−1, ¹H^(α/β) _(i−1); (2) α- and β-carbons of amino acid residuei−1, ¹³C^(α/β) _(i−1); (3) a polypeptide backbone carbonyl carbon ofamino acid residue i−1, ¹³C′_(i−i); (4) a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); and (5) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i), (b) saidselecting comprises selecting 4 chemical shift evolution periods of the6D FT NMR experiment, ¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1),and ¹³C′_(i−1), and (c) said jointly sampling comprises jointly samplingthe 4 chemical shift evolution periods in an indirect time domaindimension, t₁(¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ₁₃C^(α) _(i−1),¹³C′_(i−1)).
 40. The method according to claim 1, wherein N equals 5 andK equals 3 to conduct a (5,2)D [HBHACBCACA(CO)NHN] GFT NMR experiment,wherein (a) said sample is a protein molecule having two amino acidresidues, i and i−1, and the chemical shift values for the followingnuclei are measured: (1) α- and β protons of amino acid residue i−1,¹H^(α/β) _(i−1); (2) α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i) ₁; (3) a polypeptide backbone amide nitrogen of aminoacid residue i, ¹⁵N_(i); and (4) a polypeptide backbone amide proton ofamino acid residue i, ¹H^(N) _(i), (b) said selecting comprisesselecting 4 chemical shift evolution periods of the 5D FT NMRexperiment, ¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), and¹⁵N_(i), and (c) said jointly sampling comprises jointly sampling the 4chemical shift evolution periods in an indirect time domain dimension,t₁(¹H^(α/β) _(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹⁵N_(i)).
 41. Themethod according to claim 1, wherein N equals 6 and K equals 4 toconduct a (6,2)D [HBHACBCACACONHN] GFT NMR experiment, wherein (a) saidsample is a protein molecule having two amino acid residues, i and i−1,and the chemical shift values for the following nuclei are measured: (1)α- and β protons of amino acid residue i−1, ¹H^(α/β) _(i−1); (2) α- andβ-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); (3) a polypeptidebackbone carbonyl carbon of amino acid residue i−1, ¹³C′_(i−1); (4) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (5) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i), (b) said selecting comprises selecting 5 chemical shiftevolution periods of the 6D FT NMR experiment, ¹H^(α/β) _(i−1),¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), and ¹⁵N_(i), and (c) saidjointly sampling comprises jointly sampling the 5 chemical shiftevolution periods in an indirect time domain dimension, t₁(¹H^(α/β)_(i−1), ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), ₁₃C′_(i−1), ¹⁵N_(i)).
 42. Themethod according to claim 1, wherein N equals 5 and K equals 2 toconduct a (5,3)D [HCC,CH—COSY] GFT NMR experiment, wherein (a) thechemical shift values for the following nuclei are measured: (1) aproton, ¹H; (2) a carbon coupled to ¹H, ¹³C; and (3) a carbon coupled to¹³C, ¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled),¹H^(coupled), (b) said selecting comprises selecting 3 chemical shiftevolution periods of the 5D FT NMR experiment, ¹H, ¹³C, and¹³C^(coupled), and (c) said jointly sampling comprises jointly samplingthe 3 chemical shift evolution periods in an indirect time domaindimension, t₁(¹H, ¹³C, ¹³C^(coupled)).
 43. The method according to claim42, wherein said chemical shift evolution periods for ¹³C and¹³C^(coupled) are correlated using total correlation spectroscopy(TOCSY).
 44. The method according to claim 42, wherein (a) said sampleis a protein molecule having an amino acid residue, i, and the chemicalshift values for the following nuclei are measured: (1) a proton ofamino acid residue i, ¹H_(i); (2) a carbon of amino acid residue icoupled to ¹H_(i), ¹³C_(i); and (3) a carbon coupled to ¹³C_(i), ¹³C_(i)^(coupled); and (4) a proton coupled with ¹³C_(i) ^(coupled), ¹H_(i)^(coupled), (b) said selecting comprises selecting 3 chemical shiftevolution periods of the 5D FT NMR experiment, ¹H_(i), ¹³C_(i), and¹³C_(i) ^(coupled), and (c) said jointly sampling comprises jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H_(i), ¹³C_(i), ¹³C_(i) ^(coupled)).
 45. Themethod according to claim 44, wherein said applying radiofrequencypulses comprises applying radiofrequency pulses for a 5D FT NMRexperiment according to the scheme shown in FIG.
 13. 46. The methodaccording to claim 1, wherein N equals 5 and K equals 2 to conduct a(5,3)D [HBCBCGCDHD] GFT NMR experiment, wherein (a) said sample is aprotein molecule having an amino acid residue, i, with an aromatic sidechain, and the chemical shift values for the following nuclei aremeasured: (1) a β-proton of amino acid residue i, ¹H^(β) _(i); (2) aβ-carbon of amino acid residue i, ¹³C^(β) _(i); (3) a γ-carbon of aminoacid residue i, ¹³C^(γ) _(i); (4) a δ-carbon of amino acid residue i,¹³C^(δ) _(i); and (5) a δ-proton of amino acid residue i, ¹H^(δ) _(i),(b) said selecting comprises selecting 3 chemical shift evolutionperiods of the 5D FT NMR experiment, ¹H^(β) _(i), ¹³C^(β) _(i), and¹³C^(δ) _(i), and (c) said jointly sampling comprises jointly samplingthe 3 chemical shift evolution periods in an indirect time domaindimension, t₁(¹H^(β) _(i), ¹³C^(β) ^(i), ¹³C^(δ) _(i)).
 47. The methodaccording to claim 46, wherein said applying radio frequency pulsescomprises applying radio frequency pulses for a 5D FT NMR experimentaccording to the scheme shown in FIG.
 14. 48. The method according toclaim 1, wherein N equals 5 and K equals 3 to conduct a (5,2)D[HBCBCGCDHD] GFT NMR experiment, wherein (a) said sample is a proteinmolecule having an amino acid residue, i, with an aromatic side chain,and the chemical shift values for the following nuclei are measured: (1)a β-proton of amino acid residue i, ¹H^(β) _(i); (2) a β-carbon of aminoacid residue i, ¹³C^(β) _(i); (3) a γ-carbon of amino acid residue i;(4) a δ-carbon of amino acid residue i, ¹³C^(δ) _(i); and (5) a δ-protonof amino acid residue i, ¹H^(δ) _(i), (b) said selecting comprisesselecting 4 chemical shift evolution periods of the 5D FT NMRexperiment, ¹H^(β) _(i), ¹³C^(β) _(i), ¹³C^(γ) _(i), and ¹³C^(δ) _(i),and (c) said jointly sampling comprises jointly sampling the 4 chemicalshift evolution periods in an indirect time domain dimension, t₁(¹H^(β)_(i), ¹³C^(β) _(i), ¹³C^(γ) _(i), ¹³C^(δ) _(i)).
 49. The methodaccording to claim 1, wherein N equals 4 and K equals 2 to conduct a(4,2)D [HCCH—COSY] GFT NMR experiment, wherein (a) the chemical shiftvalues for the following nuclei are measured: (1) a proton, ¹H; (2) acarbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C, ¹³C^(coupled);and (4) a proton coupled to ¹³C^(coupled), ¹H^(coupled), (b) saidselecting comprises selecting 3 chemical shift evolution periods of the4D FT NMR experiment, ¹H, ¹³C, and ¹³C^(coupled), and (c) said jointlysampling comprises jointly sampling the 3 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H, ¹³C,¹³C^(coupled)).
 50. The method according to claim 49, wherein saidchemical shift evolution periods for ¹³C and ¹³C^(coupled) arecorrelated using total correlation spectroscopy (TOCSY).
 51. The methodaccording to claim 49, wherein (a) said sample is a protein moleculehaving an amino acid residue, i, and the chemical shift values for thefollowing nuclei are measured: (1) a proton of amino acid residue i,¹H_(i); (2) a carbon of amino acid residue i coupled to ¹H_(i), ¹³C_(i);(3) a carbon coupled to ¹³C_(i), ¹³C_(i) ^(coupled); and (4) a protoncoupled to ¹³C_(i) ^(coupled), ¹H_(i) ^(coupled), (b) said selectingcomprises selecting 3 chemical shift evolution periods of the 4D FT NMRexperiment, ¹H_(i), ¹³C_(i), and ¹³C_(i) ^(coupled), and (c) saidjointly sampling comprises jointly sampling the 3 chemical shiftevolution periods in an indirect time domain dimension, t₁(¹H_(i),¹³C_(i) ^(coupled)).
 52. The method according to claim 51, wherein saidapplying radio frequency pulses comprises applying radio frequencypulses for a 4D FT NMR experiment according to the scheme shown in FIG.15.
 53. The method according to claim 1, wherein N equals 5 and K equals3 to conduct a (5,2)D [HCCCH—COSY] GFT NMR experiment, wherein (a) thechemical shift values for the following nuclei are measured: (1) aproton ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C,¹³C^(coupled); (4) a carbon coupled to ¹³C^(coupled), ¹³C^(coupled-2);and (5) a proton coupled with ¹³C^(coupled-2), ¹H^(coupled-2), (b) saidselecting comprises selecting 4 chemical shift evolution periods of the5D FT NMR experiment, ¹H, ¹³C, ¹³C^(coupled), and ¹³C^(coupled-2), and(c) said jointly sampling comprises jointly sampling the 4 chemicalshift evolution periods in an indirect time domain dimension, t₁(¹H,¹³C, ¹³C^(coupled), ¹³C^(coupled-2)).
 54. The method according to claim53, wherein (a) said sample is a protein molecule having an amino acidresidue, i, and the chemical shift values for the following nuclei aremeasured: (1) a proton of amino acid residue i, ¹H_(i); (2) a carbon ofamino acid residue i coupled to ¹H_(i), ¹³C_(i); (3) a carbon coupled to¹³C_(i), ¹³C_(i) ^(coupled); (4) a carbon coupled to ¹³C_(i) ^(coupled),¹³C_(i) ^(coupled-2); and (5) a proton coupled with ¹³C_(i)^(coupled-2), ¹H_(i) ^(coupled-2), (b) said selecting comprisesselecting 4 chemical shift evolution periods of the 5D FT NMRexperiment, ¹H_(i), ¹³C_(i), ¹³C_(i) ^(coupled), and ¹³C_(i)^(coupled-2), and (c) said jointly sampling comprises jointly samplingthe 4 chemical shift evolution periods in an indirect time domaindimension, t₁(¹H_(i), ¹³C_(i), ¹³C_(i) ^(coupled), ¹³C_(i)^(coupled-2)).
 55. The method according to claim 1, wherein N equals 5and K equals 3 to conduct a (5,3)D [HCCCH—COSY] GFT NMR experiment,wherein (a) the chemical shift values for the following nuclei aremeasured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) acarbon coupled to ¹³C, ¹³C^(coupled); (4) a carbon coupled to¹³C^(coupled), ¹³C^(coupled-2); and (5) a proton coupled with¹³C^(coupled-2), ¹H^(coupled-2), (b) said selecting comprises selecting3 chemical shift evolution periods of the 5D FT NMR experiment, ¹H, ¹³C,and ¹³C^(coupled), and (c) said jointly sampling comprises jointlysampling the 3 chemical shift evolution periods in an indirect timedomain dimension, t₁(¹H, ¹³C, ¹³C^(coupled)).
 56. The method accordingto claim 55, wherein (a) said sample is a protein molecule having anamino acid residue, i, and the chemical shift values for the followingnuclei are measured: (1) a proton of amino acid residue i, ¹H_(i); (2) acarbon of amino acid residue i coupled to ¹H_(i), ¹³C_(i); (3) a carboncoupled to ¹³C_(i), ¹³C_(i) ^(coupled); (4) a carbon coupled to ¹³C_(i)^(coupled), ¹³C_(i) ^(coupled-2); and (5) a proton coupled with ¹³C_(i)^(coupled-2), ¹H_(i) ^(coupled-2), (b) said selecting comprisesselecting 3 chemical shift evolution periods of the 5D FT NMRexperiment, ¹H_(i), ¹³C_(i), and ¹³C_(i) ^(coupled), (c) said jointlysampling comprises jointly sampling the 3 chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H_(i), ¹³C_(i),¹³C_(i) ^(coupled)).
 57. A method for sequentially assigning chemicalshift values of an α-proton, ¹H^(α), an α-carbon, ¹³C^(α), a polypeptidebackbone carbonyl carbon, ¹³C′, a polypeptide backbone amide nitrogen,¹⁵N, and a polypeptide backbone amide proton, ¹H^(N), of a proteinmolecule comprising: providing a protein sample; conducting a set of Gmatrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiments on the protein sample comprising: (1) a (5,2)D [HACACONHN]GFT NMR experiment to measure and connect the chemical shift values ofthe α-proton of amino acid residue i−1, ¹H^(α) _(i−1), the α-carbon ofamino acid residue i−1, ¹³C^(α) _(i−1), the polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i−1), the polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i), and thepolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i)and (2) a (5,2)D [HACA,CONHN] GFT NMR experiment to measure and connectthe chemical shift values of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1),the polypeptide backbone amide nitrogen of amino acid residue i−1,¹⁵N_(i−1), and the polypeptide backbone amide proton of amino acidresidue i−1, ¹H^(N) _(i−1); and obtaining sequential assignments of thechemical shift values of ¹H^(α), ¹³C^(α,) ¹³C′, ¹⁵N, and ¹H^(N) by (i)matching the chemical shift values of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and¹³C′_(i−1) measured by said (5,2)D [HACACONHN] GFT NMR experiment withthe chemical shift values of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and¹³C′_(i−1) measured by said (5,2)D [HACA,CONHN] GFT NMR experiment, (ii)using the chemical shift values of ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and¹³C′_(i−1) to identify the type of amino acid residue i−1, and (iii)mapping sets of sequentially connected chemical shift values to theamino acid sequence of the polypeptide chain and using said chemicalshift values to locate secondary structure elements within thepolypeptide chain.
 58. The method according to claim 57 furthercomprising: subjecting the protein sample to nuclear Overhauserenhancement spectroscopy (NOESY) to deduce the tertiary structure of theprotein molecule.
 59. The method according to claim 57 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure scalar coupling constants to deduce the tertiary structure ofthe protein molecule.
 60. The method according to claim 57 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure residual dipolar coupling constants to deduce the tertiarystructure of the protein molecule.
 61. A method for sequentiallyassigning chemical shift values of an α-proton, ¹H^(α), an α-carbon,¹³C^(α), a polypeptide backbone carbonyl carbon, ¹³C′, a polypeptidebackbone amide nitrogen, ¹⁵N, and a polypeptide backbone amide proton,¹H^(N), of a protein molecule comprising: providing a protein sample;conducting a set of G matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiments on the protein sample comprising:(1) a (5,3)D [HACACONHN] GFT NMR experiment to measure and connect thechemical shift values of the α-proton of amino acid residue i−1, ¹H^(α)_(i−1), the α-carbon of amino acid residue i−1, ¹³C^(α) _(i−1), thepolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i−1), the polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i), and the polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i) and (2) a (5,3)D [HACA,CONHN] GFT NMRexperiment to measure and connect the chemical shift values of ¹H^(α)_(i−1), ¹³C^(α) _(i−1), ¹³C′_(i−1), the polypeptide backbone amidenitrogen of amino acid residue i−1, ¹⁵N_(i−1), and the polypeptidebackbone amide proton of amino acid residue i−1, ¹H^(N) _(i−1); andobtaining sequential assignments of the chemical shift values of ¹H^(α),¹³C^(α), ¹³C′, ¹⁵N, and ¹H^(N) by (i) matching the chemical shift valuesof ¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) measured by said (5,3)D[HACACONHN] GFT NMR experiment with the chemical shift values of ¹H^(α)_(i−1) , ¹³C^(α) _(i−1), and ¹³C′_(i−l) measured by said (5,3)D[HACA,CONHN] GFT NMR experiment, (ii) using the chemical shift values of¹H^(α) _(i−1), ¹³C^(α) _(i−1), and ¹³C′_(i−1) to identify the type ofamino acid residue i−1, and (iii) mapping sets of sequentially connectedchemical shift values to the amino acid sequence of the polypeptidechain and using said chemical shift values to locate secondary structureelements within the polypeptide chain.
 62. The method according to claim61 further comprising: subjecting the protein sample to nuclearOverhauser enhancement spectroscopy (NOESY) to deduce the tertiarystructure of the protein molecule.
 63. The method according to claim 61further comprising: subjecting the protein sample to NMR experimentsthat measure scalar coupling constants to deduce the tertiary structureof the protein molecule.
 64. The method according to claim 61 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure residual dipolar coupling constants to deduce the tertiarystructure of the protein molecule.
 65. A method for sequentiallyassigning chemical shift values of α- and β-carbons, ¹³C^(α/β), apolypeptide backbone carbonyl carbon, ¹³C′, a polypeptide backbone amidenitrogen, ¹⁵N, and a polypeptide backbone amide proton, ¹H^(N), of aprotein molecule comprising: providing a protein sample; conducting aset of G matrix Fourier transformation (GFT) nuclear magnetic resonance(NMR) experiments on the protein sample comprising: (1) a (4,3)D[CBCACONHN] GFT NMR experiment to measure and connect the chemical shiftvalues of the α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i−1), the polypeptide backbone carbonyl carbon of amino acid residuei−1, ¹³C′_(i−1), the polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i), and the polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i) and (2) a (4,3)D [CBCA,CONHN] GFT NMRexperiment to measure and connect the chemical shift values of ¹³C^(α/β)_(i−1), ¹³C′_(i−1), the polypeptide backbone amide nitrogen of aminoacid residue i−1, ¹⁵N_(i−1), and the polypeptide backbone amide protonof amino acid residue i−1, ¹H^(N) _(i−1); and obtaining sequentialassignments of the chemical shift values of ¹³C^(α/β), ¹³C′, ¹⁵N, and¹H^(N) by (i) matching the chemical shift values of ¹³C^(α/β) _(i−1) and¹³C′_(i−1) measured by said (4,3)D [CBCACONHN] GFT NMR experiment withthe chemical shift values of ¹³C^(α/β) _(i−1) and ¹³C′_(i−1) measured bysaid (4,3)D [CBCA,CONHN] GFT NMR experiment, (ii) using the chemicalshift values of ¹³C^(α/β) _(i−1) and ¹³C′_(i−1) to identify the type ofamino acid residue i−1, and (iii) mapping sets of sequentially connectedchemical shift values to the amino acid sequence of the polypeptidechain and using said chemical shift values to locate secondary structureelements within the polypeptide chain.
 66. The method according to claim65 further comprising: subjecting the protein sample to nuclearOverhauser enhancement spectroscopy (NOESY) to deduce the tertiarystructure of the protein molecule.
 67. The method according to claim 65further comprising: subjecting the protein sample to NMR experimentsthat measure scalar coupling constants to deduce the tertiary structureof the protein molecule.
 68. The method according to claim 65 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure residual dipolar coupling constants to deduce the tertiarystructure of the protein molecule.
 69. A method for sequentiallyassigning chemical shift values of α- and β-carbons, ¹³C^(α/β), apolypeptide backbone amide nitrogen, ¹⁵N, and a polypeptide backboneamide proton, ¹H^(N), of a protein molecule comprising: providing aprotein sample; conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein samplecomprising: (1) a (4,3)D [HNNCACBCA] GFT NMR experiment to measure andconnect the chemical shift values of the α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i−1), the α-carbon of amino acid residue i−1,¹³C^(α) _(i−1), the polypeptide backbone amide nitrogen of amino acidresidue i−1, ¹⁵N_(i−1), and the polypeptide backbone amide proton ofamino acid residue i−1, ¹H^(N) _(i−1) and (2) a GFT NMR experimentselected from the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMRexperiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D[HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connect thechemical shift values of ¹³C^(α/β) _(i−1), ¹³C^(α) _(i−1), thepolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i),and the polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i); and obtaining sequential assignments of the chemical shiftvalues of ¹³C^(α/β), ¹⁵N, and ¹H^(N) by (i) matching the chemical shiftvalues of ¹³C^(α/β) _(i−1) measured by said GFT NMR experiment selectedfrom the group consisting of a (4,3)D [HNN(CO)CACBCA] GFT NMRexperiment, a (4,3)D [CBCACA(CO)NHN] GFT NMR experiment, and a (5,3)D[HBHACBCACA(CO)NHN] GFT NMR experiment with the chemical shift values of¹³C_(α/β) _(i−1) measured by said (4,3)D [HNNCACBCA] GFT NMR experiment,(ii) using the chemical shift values of ¹³C^(α/β) _(i−1) to identify thetype of amino acid residue i−1, and (iii) mapping sets of sequentiallyconnected chemical shift values to the amino acid sequence of thepolypeptide chain and using said chemical shift values to locatesecondary structure elements within the polypeptide chain.
 70. Themethod according to claim 69 further comprising: subjecting the proteinsample to nuclear Overhauser enhancement spectroscopy (NOESY) to deducethe tertiary structure of the protein molecule.
 71. The method accordingto claim 69 further comprising: subjecting the protein sample to NMRexperiments that measure scalar coupling constants to deduce thetertiary structure of the protein molecule.
 72. The method according toclaim 69 further comprising: subjecting the protein sample to NMRexperiments that measure residual dipolar coupling constants to deducethe tertiary structure of the protein molecule.
 73. A method forassigning chemical shift values of γ-, δ-, and ε-aliphatic sidechainprotons, ¹H_(γ/δ/ε), and chemical shift values of γ-, δ-, andε-aliphatic sidechain carbons located peripheral to β-carbons,¹³C^(γ/δ/ε), of a protein molecule comprising: providing a proteinsample; conducting a set of G matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiments on the protein samplecomprising: (1) a (5,3)D [HCC,CH—COSY] GFT NMR experiment to measure andconnect the chemical shift values of a proton of amino acid residue i−1,¹H_(i−1), a carbon of amino acid residue i−1 coupled to ¹H_(i−1),¹³C_(i−1), a carbon coupled to ¹³C_(i−1), ¹³C_(i−1) ^(coupled), and aproton coupled to ¹³C_(i−1) ^(coupled), ¹H_(i−1) ^(coupled), and (2)a(5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment to measure and connectthe chemical shift values of α- and β-protons of amino acid residue i−1,¹H^(α/β) _(i−1), and α- and β-carbons of amino acid residue i−1,¹³C^(α/β) _(i−1); and obtaining assignments of the chemical shift valuesof ¹H^(γ/δ/ε) and ¹³C^(γ/δ/ε) by (i) identifying ¹H_(i−1), ¹³C_(i−1),¹³C_(i−1) ^(coupled), and ¹H_(i−1) ^(coupled) measured by said (5,3)D[HCC,CH—COSY] GFT NMR experiment as ¹H^(α) _(i−1), ¹³C^(α) _(i−1),¹³C^(β) _(i−1), and ¹H^(β) _(i−1), respectively, and thereby matchingthe chemical shift values of ¹H^(α/β) _(i−1), and ¹³C^(α/β) _(i−1) withthe chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β) _(i−1)measured by said (5,3)D HBHACBCACA(CO)NHN] GFT NMR experiment, and (ii)using the chemical shift values of ¹H^(α/β) _(i−1) and ¹³C^(α/β) _(i−1)in conjunction with other chemical shift connections from said (5,3)D[HCC,CH—COSY] GFT NMR experiment to measure the chemical shift values of¹H^(γ/δ/ε) _(i−1) and ¹³C^(γ/δ/ε) _(i−1).
 74. The method according toclaim 73 further comprising: subjecting the protein sample to nuclearOverhauser enhancement spectroscopy (NOESY) to deduce the tertiarystructure of the protein molecule.
 75. The method according to claim 73further comprising: subjecting the protein sample to NMR experimentsthat measure scalar coupling constants to deduce the tertiary structureof the protein molecule.
 76. The method according to claim 73 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure residual dipolar coupling constants to deduce the tertiarystructure of the protein molecule.
 77. A method for assigning chemicalshift values of γ-, δ-, and ε-aliphatic sidechain protons, ¹H^(γ/δ/ε),and chemical shift values of γ-, δ-, and ε-aliphatic sidechain carbonslocated peripheral to β-carbons, ¹³C^(γ/δ/ε), of a protein moleculecomprising: providing a protein sample; conducting a set of G matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiments on the protein sample comprising: (1) a (4,2)D [HCCH—COSY]GFT NMR experiment to measure and connect the chemical shift values of aproton of amino acid residue i−1, ¹H_(i−1), a carbon of amino acidresidue i−1 coupled to ¹H_(i−1), ¹³C_(i−1), a carbon coupled to¹³C_(i−1), ¹³C_(i−1) ^(coupled), and a proton coupled to ¹³C_(i−1)^(coupled), ¹H_(i−1) ^(coupled), and (2) a (5,3)D [HBHACBCACA(CO)NHN]GFT NMR experiment to measure and connect the chemical shift values ofα- and β-protons of amino acid residue i−1, ¹H^(α/β) _(i−1), and α- andβ-carbons of amino acid residue i−1, ¹³C^(α/β) _(i−1); and obtainingassignments of the chemical shift values of ¹H^(γ/δ/ε) and ¹³C^(γ/δ/ε)by (i) identifying ¹H_(i−1), ¹³C_(i−1), ¹³C_(i−1) ^(coupled), and¹H_(i−1) ^(coupled) measured by said (4,2)D [HCC,H—COSY] GFT NMRexperiment as ¹H^(α) _(i−1), ¹³C^(α) _(i−1), ¹³C^(β) _(i−1), and ¹H^(β)_(i−1), respectively, and thereby matching the chemical shift values of¹H^(α/β) _(i−1) and ¹³C^(α/β) _(i−1) with the chemical shift values of¹H^(α/β) _(i−1) and ¹³C^(α/β) _(i−1) measured by said (5,3)DHBHACBCACA(CO)NHN] GFT NMR experiment, and (ii) using the chemical shiftvalues of ¹H^(α/β) _(i−1) and ¹³C^(α/β) _(i−1) in conjunction with otherchemical shift connections from said (4,2)D [HCCH—COSY] GFT NMRexperiment to measure the chemical shift values of ¹H^(γ/δ/ε) _(i−1) and¹³C^(γ/δ/ε) _(i−1).
 78. The method according to claim 77 furthercomprising: subjecting the protein sample to nuclear Overhauserenhancement spectroscopy (NOESY) to deduce the tertiary structure of theprotein molecule.
 79. The method according to claim 77 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure scalar coupling constants to deduce the tertiary structure ofthe protein molecule.
 80. The method according to claim 77 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure residual dipolar coupling constants to deduce the tertiarystructure of the protein molecule.
 81. A method for assigning chemicalshift values of a γ-carbon, ¹³C^(γ), a δ-carbon, ¹³C^(δ), and aδ-proton, ¹H^(δ), of an amino acid residue containing an aromatic spinsystem in a protein molecule comprising: providing a protein sample;conducting a set of G matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiments on the protein sample comprising:(1) a (5,3)D [HBCBCGCDHD] GFT NMR experiment to measure and connect thechemical shift values of a β-proton of amino acid residue i−1, ¹H^(β)_(i−1), a β-carbon of amino acid residue i−1, ¹³C^(β) _(i−1), a γ-carbonof amino acid residue i−1, ¹³C^(γ) _(i−1), a δ-carbon of amino acidresidue i−1, ¹³C^(δ) _(i−1), and a δ-proton of amino acid residue i−1,¹H^(δ) _(i−1), and (2) a (5,3)D [HBHACBCACA(CO)NHN] GFT NMR experimentto measure and connect the chemical shift values of ¹H^(β) _(i−1) and¹³C^(β) _(i−1); and obtaining assignments of the chemical shift valuesof ¹³C^(γ), ¹³C^(δ), and ¹H^(δ) by (i) matching the chemical shiftvalues of ¹H^(β) _(i−1) and ¹³C^(β) _(i−1) measured by said (5,3)DHBCBCACA(CO)NHN GFT NMR experiment with the chemical shift values of¹H^(β) _(i−1) and ¹³C^(β) _(i−1) measured by said (5,3)D [HBCBCGCDHD]GFT NMR experiment, and (ii) using the chemical shift values of ¹³C^(γ),¹³C^(δ), and ¹H^(δ) to identify the type of amino acid residuecontaining the aromatic spin system.
 82. The method according to claim81 further comprising: subjecting the protein sample to nuclearOverhauser enhancement spectroscopy (NOESY) to deduce the tertiarystructure of the protein molecule.
 83. The method according to claim 81further comprising: subjecting the protein sample to NMR experimentsthat measure scalar coupling constants to deduce the tertiary structureof the protein molecule.
 84. The method according to claim 81 furthercomprising: subjecting the protein sample to NMR experiments thatmeasure residual dipolar coupling constants to deduce the tertiarystructure of the protein molecule.
 85. A method for assigning chemicalshift values of aliphatic and aromatic protons and aliphatic andaromatic carbons of an amino acid residue containing aliphatic andaromatic spin systems in a protein molecule comprising: providing aprotein sample; conducting a set of G matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiments on the protein samplecomprising: (1) a first GFT NMR experiment, which is selected from thegroup consisting of a (5,3)D [HCC,CH—COSY] GFT NMR experiment, a (4,2)D[HCCH—COSY] GFT NMR experiment, a (5,2)D [HCCCH—COSY] GFT NMRexperiment, and a (5,3)D [HCCCH—COSY] GFT NMR experiment and is acquiredfor the aliphatic spin system, to measure and connect the chemical shiftvalues of α- and β-protons of amino acid residue i, ¹H^(α/β) _(i), α-and β-carbons of amino acid residue i, ¹³C^(α/β) _(i), a γ-carbon ofamino acid residue i, ¹³C^(γ) _(i), and (2) a second GFT NMR experiment,which is selected from the group consisting of a (5,3)D [HCC,CH—COSY]GFT NMR experiment, a (4,2)D [HCCH—COSY] GFT NMR experiment, a (5,2)D[HCCCH—COSY] GFT NMR experiment, and a (5,3)D [HCCCH—COSY] GFT NMRexperiment and is acquired for the aromatic spin system, to measure andconnect the chemical shift values of ¹³C^(γ) _(i) and other aromaticprotons and carbons of amino acid residue i; and obtaining assignmentsof the chemical shift values of the aliphatic and aromatic protons andaliphatic and aromatic carbons by matching the chemical shift value of¹³C^(γ) _(i) measured by said first GFT NMR experiment with the chemicalshift value of ¹³C^(γ) _(i) measured by said second GFT NMR experiment.86. The method according to claim 85, wherein said conducting a set ofGFT NMR experiments is carried out by using ¹³C^(γ) steady statemagnetization to generate first order central peaks.
 87. The methodaccording to claim 85 further comprising: subjecting the protein sampleto nuclear Overhauser enhancement spectroscopy (NOESY) to deduce thetertiary structure of the protein molecule.
 88. The method according toclaim 85 further comprising: subjecting the protein sample to NMRexperiments that measure scalar coupling constants to deduce thetertiary structure of the protein molecule.
 89. The method according toclaim 85 further comprising: subjecting the protein sample to NMRexperiments that measure residual dipolar coupling constants to deducethe tertiary structure of the protein molecule.
 90. A method forobtaining assignments of chemical shift values of ¹H, ¹³C, and ¹⁵N of aprotein molecule comprising: providing a protein sample; and conductingfive G matrix Fourier transformation (GFT) nuclear magnetic resonance(NMR) experiments on the protein sample, wherein (1) a first experimentis a (4,3)D [HNNCACBCA] GFT NMR experiment for obtaining intraresiduecorrelations of chemical shift values; (2) a second experiment is a(5,3)D [HBHACBCACA(CO)NHN] GFT NMR experiment for obtaining interresiduecorrelations of chemical shift values; (3) a third experiment is a(5,3)D [HCC,CH—COSY] GFT NMR experiment for obtaining assignments ofaliphatic sidechain chemical shift values; (4) a fourth experiment is a(5,3)D [HBCBCGCDHD] GFT NMR experiment for linking chemical shift valuesof aliphatic protons, ¹H^(β) and ¹³C^(β), and aromatic protons, ¹³C^(δ)and ¹H^(δ); and (5) a fifth experiment is a (4,2)D [HCCH—COSY] GFT NMRexperiment for obtaining assignments of aromatic sidechain chemicalshift values.
 91. The method according to claim 90 further comprising:subjecting the protein sample to nuclear Overhauser enhancementspectroscopy (NOESY) to deduce the tertiary structure of the proteinmolecule.
 92. The method according to claim 90 further comprising:subjecting the protein sample to NMR experiments that measure scalarcoupling constants to deduce the tertiary structure of the proteinmolecule.
 93. The method according to claim 90 further comprising:subjecting the protein sample to NMR experiments that measure residualdipolar coupling constants to deduce the tertiary structure of theprotein molecule.